could I use state laws such as Washington State RCW 9.61, for instance, to pursue civil action against someone who say disrupts, convludes, degrades, or otherwise attacks my home network connection over DSL
RCW 9.61 concerns only "making a telephone call," not disrupting, convluding(?), degrading, or otherwise attacking anything. In a DSL connection, the only person establishing the connection ("making" the "call") is the DSL subscriber. A closer analogy to telephone communication would be somehow impeding a victim's ability to make a telephone call.
Furthermore, to be covered, a telephone call must disturb the recipient in some way that engages item (a), (b), or (c). DSL is designed to allow normal telephone communication to continue while the DSL connection is underway: a DSL subscriber can make and receive telephone calls normally. It's difficult to see how a malicious actor could disrupt a target's internet connection by making a call. If it were somehow possible, the phone calls might incidentally trigger this statute (for example if they are repeated -- see item (b)), but the attack itself on the target's internet connection would probably have to be prosecuted under laws criminalizing interference with telecommunications more generally.
While it's certainly possible that there are circumstances under which a DSL connection might be considered a telephone call, it's hard to imagine how they could apply to RCW 9.61. If they could, the statute would cover a malicious actor establishing a DSL connection to a victim (for one of the purposes outlined in (a), (b), or (c)), and that's not even possible.
If you're asking whether this law could be involved because the person who's attacking your network is a DSL subscriber rather than having, say, a fiber optic connection, then I still doubt it. Even if establishing a DSL connection can be said to be making a phone call, the recipient of the call in this case is the telecommunication company as an internet service provider, whereas the statute only covers phone calls made "to such other person" -- to the victim of the harassment.