It was the power supply! The new one arrived yesterday and I swapped it out and it's working again. What a relief! It still runs slow as hell though.
In the meantime, I started setting up a separate PC that I'm probably going to swap in if I can figure out how to power it on with an external button. It's a SFF HP Elitedesk that doesn't have any motherboard pins, which is super annoying. So I think I need to solder 2 wires to the board where the current power button is located? Does that sound correct? This is what the power button looks like inside the Elitedesk:


The two thick posts in the first image are what I think need to be shorted to power on the PC. I used my multimeter set to continuity and got a beep when I connected them. You can see underneath the motherboard where the solder points are. I think I'll be OK because it's a bit of a mess so I just need to heat up what's there and connect a wire to each contact point. Does that seem correct?
Also, I forgot what a huge pain it is to set up a PC for this cabinet with Hyperspin and RocketLauncher and Hypermarquee. I would use something easier instead of Hyperspin but I can't figure out how to
precisely locate the marquee window on the marquee monitor. Launchbox and Attract Mode just center the marquee image on the second screen and I need a window I can drag to the correct location. I would also need to figure out
how to map the Pause button to also work for "Exit to Gamelist" if you hold it down for 3 seconds. RocketLauncher has a setting for this.
So... anyone got any suggestions?
