Can a brown dwarf be ignited?
The simple answer is "yes, but it won't last long."
The first part is "what is the minimum mass for a star", and that's about 75 times the mass of Jupiter. We know stars somewhat above this limit, like AB Doradus C at 93 times Jupiter mass, or "Mj". This makes a brown dwarf basically anything from 1 Mj to 75, although it's not a strong definition and most put the lower limit at 13 Mj. So for the rest, let's use 75 Mj as "our object".
Dwarfs at this upper limit do undergo fusion, for a period of time at least. This is when they first form, and still contain deuterium, enough for the D-D reaction which requires lower temperatures than the p-p reaction. The D-D fusion causes it to heat up, which is captured in the dwarf and is then slowly lost over time. As it loses heat it will contract, and in theory would at some point reach the conditions needed for p-p, but that does not occur because the collapse stops due to the electron degenerate core. That's what defines it being a brown dwarf at the upper limit.
Unfortunately I can't find a simple explanation of the amount of heat that will be retained, nor how fast it will be released. But for a while at least, you'll have a "star like" object that is hot and cooling into space.
So one could imagine a magical system that compresses your large object to p-p conditions and then releases it again. After being released, the object would expand and the fusion would go out again, just as it did for D-D. But during that period it would also generate heat, as it did the first time, and that will take time to "burn off" again.
So it depends on how long you want all of this to happen. If you want to burn a nearby planet, maybe this will work. If you want to turn a planetary system habitable, not so much unless you assume Microcosmic God.