Distracted by the Shine
Starting at least in the 1st century BC, a standard interpretation of this story has been that Danae granted Zeus her favours in exchange for gold, i.e. she was seduced by the offer of money.
Recorded in the Greek Anthology, Parmenion might be earliest example of an author who contrasts the possibility of rape with the idea that it was a consensual trade when he says, addressing Zeus in AP 5.33 = GPh 1:
You flew like gold rain to Danae, Olympian, so that the girl
would be won over by the gift, and not tremble before Cronides ["Cronus'
Son"].
Some four centuries later a Latin writer, namely Fulgentius, corroborates Parmenion's statement, saying of Danae in Mythologies 1.19 that:
the god Jove [i.e. Jupiter, the Roman Zeus] showed her wealth and tricked with gold one he had been
unable to trick by force.
Fast-forward to the 1500s AD, about a millennium later, and the Italian poet Giovanni Andrea dell’ Anguillara provides the first particularly clear instance I have been able to find of Danae's emotional state upon meeting Zeus. According to Cathy Santore's 1991 article "Danaë: The Renaissance Courtesan's Alter Ego,"1
When Anguillara retells Ovid's Metamorphoses he takes the liberty of embellishing
the tale to suit his fancy. He puts Danaë first in a garden then a
loggia and finally in her room where Jove appears in bodily form. Her
first reaction is to flee, but the god sweet talks her and shows her
so much gold that he finally got what he wanted...
Violence on Stage?
Several tragedies and comedies entitled Danae were written in ancient times, featuring the character in question. All of them are now either completely lost or survive only in fragmentary form. Certain scholars seem to think that the remains of these plays might reveal a version of the tale in which Danae suffers an assault by Zeus.
In the 300s BC, Eubulus wrote a comedy entitled Danae. Maria Kanellou says2 that in Fragment 22 K-A of this play:
it is most probably Danae who complains, after her rape, of Zeus’
merciless brutality (ὅς με κλάουσαν τότε | οὐκ ἠλέησεν, ‘who did
not show mercy to me when I was crying’).
According to Ioanna Karamanou the "fragment presents Danae as complaining of being a victim of cruelty" and that:
It has been widely supposed that the incident to which Danae is
referring is her rape by Zeus. I think that such an interpretation is
plausible, considering that it is Zeus whom she blames for her
misfortune in fr. 47a. 783-4 R. of the Dictyulci... and who is also
the addressee of her plea in Simonides’ poem.3
This would be more conclusive except for the fact that we do not actually know for sure who is speaking here or what s\he might be referring to, nor even the precise context thereof.
The Dictyulci ("Net-Haulers") to which Karamanou refers is yet another fragmentary comedy, this one a satyr-play by Aeschylus. We have a much better idea of what is going in it than in Eubulus' Danae (since its fragments are bigger).
In the referenced passage, Danae and her little son Perseus have landed on the island of Seriphos and are being harassed by the god Seilenus and his gang of Satyrs. Terrified, Danae prays to Zeus for help, "for you were guilty of the greater fault, but it is I who have paid the full penalty. I call upon you to set things right!"
Ancient Visual Arts Considerations
Rather less regarding forcefulness or precious metal, Daniel Ogden goes more into the question of Danae's actual feelings in his 2008 book Perseus (Routledge: Taylor & Francis Group, London & New York). On p. 18 he notes that Pherecydes of Athens
is the earliest source to describe Zeus' access to Danae in any
detail. He implies that Zeus... transformed himself into golden rain
merely for the purpose of getting through the skylight, but then
reverted to humanoid form in order to have sex with the girl
(Pherecydes FGH 3 fr. 26 = fr. 10 Fowler)... But the remainder
of the literary sources imply that Zeus retained the form of golden
rain to flow directly into Danae's loins, as a sort of golden sperm...
And this indeed is the way artists liked to portray the scene, with a
shower of golden rain heading straight for Danae's lap (LIMC Danae
nos. 1-39, the earliest of which dates from ca. 490 BC). But for all
that he impregnated her in the form of pure seed, Danae was evidently
not denied sexual pleasure in the congress. In many images, from the
mid-fifth century onwards, she actively welcomes the seed into her lap
by holding her dress out of the way to receive it (LIMC Danae nos.
7, 8, 9,✭ 19, 26, 33) or alternatively uses the folds of her dress to
collect it (LIMC Danae nos. 5, 10, 12, 31). In some her head is
actually thrown back in ecstasy (note especially the
mid-fourth-century BC chalcedony intaglio, LIMC Danae no. 11).✭✭
✭ Ogden inserts a reference here to a drawing of this vase (above), appearing on p. 14 of his book.
✭✭ The 4th-century BC intaglio mentioned by Ogden (© The State Hermitage Museum, St. Petersburg)
Sophocles' Danae
Ogden also, however, briefly considers (on p. 15 of his book) the sole significant scrap of Sophocles' tragedy Danae which has survived the ravages of time: Fragment 165.
Amongst the fragments of the Danae we may find Acrisius' voice in
the phrase, 'I don't know about the rape. But one thing I do know is
that I am done for if this child lives'...
Quoting the text in its original Greek, Karamanou comments4 that:
(οὐκ οἶδα τὴν σὴν πεῖραν· ἓν δ᾽ ἐπίσταμαι·/ τοῦ παιδὸς ὄντος τοῦδ᾽ ἐγώ
διόλλυμαι)... was evidently spoken by Acrisius rejecting Danae’s
possible allegation that she was the victim of forcible usage.
Odgen is rather loosely paraphrasing when he uses the word "rape", though, which is how he has translated πεῖραν (peîran), which simply means "attempt" or "trial", such as in Hugh Lloyd-Jones' translation: "I do not know what you mean by an 'attempt'".5
From the narrative context, it seems very reasonable, as Ogden and Karamanou both say, that it is most likely Acrisius here speaking about the young boy Perseus. As for the matter of the πεῖραν, however, it is certainly speculative to conclude that this "attempt" must mean "rape." It perhaps is what Sophocles meant by it, but we have nothing apart from that conjecture to lean on in this case.
Euripides' Danae
Having said all of that, we do have the report of a writer from around the end of the Late Antique period and beginning of the Middle Ages, named John Malalas, who, in his Chronicle 2.34-35, uses less ambiguous language implying lack of consent, as he condenses the two ideas about Danae being overwhelmed with a payment of wealth, and her being taken more directly by force.
According to the translation of the passage6
by the Australian Association for Byzantine Studies:
The most learned Euripides recounted a myth about her, in the plot of
his play, that Danae was put into a chest and thrown into the sea,
after she was ravished by Zeus who had been transformed into gold. The
most learned Bouttios, the historical chronicler, stated that, when
Danae was in her chamber situated by the sea… Zeus persuaded her with
a large sum of gold and was able to win her over; he carried her off
as she was very beautiful and seduced her. He had by her the son named
Perseus…
The words translated here as "ravished" and "seduced", in both the Greek and Latin versions of the text, could also be rendered as "[utterly] corrupted", "defiled" or "violated".
The Imprisonment Itself
As to whether Danae would have gone into her sequestration willingly or otherwise, the ancient sources leave us with even less material than we have for the subject of choices in her encounter with Zeus. In other words, they say pretty much nothing on the issue, and we are left to speculate based on whatever our own sentiments about this might be.
I would guess that Danae was none too enthusiastic about being locked up. Moreover, with the heavy emphasis—throughout the story's coverage since ancient times up until the Renaissance—upon the idea that Zeus paid Danae in gold currency in order to obtain his desire, one might wonder what a prisoner like Danae could need money for.
The only answer I could come up with is that she wished to attempt an escape using these funds. And as it so happens, this is the same conclusion arrived at by the earliest source I have come across for an answer to this part of your inquiry, namely Giovanni Boccaccio's Genealogy of the Gods of the Gentiles (whose first version was completed in 1360 AD). In Book 2, Ch. 33 of this work, Boccaccio cites a certain Theodontius, saying that, according to him:
Danaë, being loved by Jove, and knowing that out of fear her father
had condemned her to perpetual imprisonment, in order to escape and
secretly take flight, made a bargain with Jove at the price of
intercourse with him.7
According to Wikipedia, Boccaccio's Genealogy quotes this Theodontius extensively but he "is otherwise almost unknown... Some authorities think Boccaccio invented him. Carlo Landi argued... that Boccaccio's Theodontius was a Campanian philosopher, from between the 9th and 11th centuries."
In the first part of the aforementioned passage of the Genealogy 2.33, Boccaccio allegorises Danae's encounter with Zeus using almost exactly the same word employed in the Latin version of Malalas' Chronicle to describe the incident as corruption/ violation. Going by Jon Solomon's translation8 thereof:
[T]hat Jupiter flowed as gold through the roof tiles, should be
understood as a maiden's chastity violated by gold, and since there
was no way for the illicit lover to enter by the door, he furtively
climbed to the roof and there let himself down into the bedchamber of
the maiden.
Notes
1. In the Zeitschrift für Kunstgeschichte 54. Bd., H. 3, pp. 412-427. (The dell’ Anguillara quotation is taken from p. 417.)
2. The quote is taken from p. 264 of Greek Epigram from the Hellenistic to the Early Byzantine Era, Edited by Maria Kanellou, Ivana Petrovic, & Chris Carey (2019), Oxford University Press, United Kingdom.
The relevant section is Ch. 15 of this book (pp. 249-271), written by Kanellou, and entitled "Mythological Burlesque and Satire in Greek Epigram—A Case Study: Zeus’ Seduction of Danae."
3. From p. 19 of her January 2005 Doctoral Thesis "A Commentary on Euripides' Danae and Dictys" in University College London's Department of Greek and Latin, Published by ProQuest LLC, 2013, Ann Arbor, MI.
4. On p. 12 of her book Euripides - Danae and Dictys: Introduction, Text and Commentary (2012), De Gruyter, Leipzig.
5. From p. 67 of his Loeb Classical Library book Sophocles: Fragments (2003), Cambridge, Massachusetts & London, England.
6. See p. 17 of The Chronicle of John Malalas: A Translation by Elizabeth Jeffreys, Michael Jeffreys and Roger Scott with Brian Croke, Jenny Ferber, Simon Franklin, Alan James, Douglas Kelly, Ann Moffatt, Ann Nixon (The Australian Association for Byzantine Studies: Byzantina Australiensia 4, 1986, Melbourne).
7. Translation taken from a quotation by Madlyn Millner Kahr in her article "Danaë: Virtuous, Voluptuous, Venal Woman" in The Art Bulletin Vol. 60, No. 1 (Mar., 1978), pp. 43-55 (specifically p. 44).
8. Pp. 246-249 of Giovanni Boccaccio: Genealogy of the Pagan Gods, Vol. 1 • Books I-V, Edited and Translated by Jon Solomon, The I Tatti Renaissance Library, Harvard University Press, Cambridge, MA, & London, England, 2011
