So I have reason to suspect the case is fucky (grounding problems with the USB), and this feels like either a motherboard or cpu problem.
The cpu is like 5 years old, the motherboard only 2.
Could also, in theory, be ram?

So I'll need to memtest it, and also try watching the temperatures while it runs. I've never had cooling problems before, but the way it kept getting worse when I rebooted it smells like cooling.

@foone
The most common failures are power supply and ram, followed by CPU, and finally motherboard. Motherboard failures are typically damaged components.
A damaged power supply would have a similar signature to what you're seeing. Damaged motherboard typically results in the board not booting at all (you'd never make it to a login screen). Same with CPU.
(I spent years repairing motherboard engineering samples)