Ok, I've gone the PSU route, since that's the easiest to manage right now. It also makes some sense, given the symptoms of a failing PSU. On top of that, I've been having trouble getting it to turn on lately. Figured it was just the button on the case given that it used to be at floor level and from time to time I'd just bop it with my foot to turn it on. Thought it was a bit messed up and worn out, and that's why it was difficult to turn on. I grabbed a spare PSU I had sitting around and tossed it in. Turned on right away without having to fiddle with the power button. I'll run the machine through its paces, see if that takes care of the issue.
I've had PSUs fail on me in the past, but not like this. In the 20+ years I've been (re)building PCs they've always just flat out failed altogether. This would be the first time I've had one fail in this manner. The kicker of it is that when connecting up my PSU tester, this supply is just fine according to it. I guess it doesn't put enough load on it to trigger a fail condition, it just tells you if each of the connector types is putting out correct voltages.