Project: Reviving an HP E-Vectra SFF Desktop PC

Not surprisingly, https://en.wikipedia.org/wiki/Capacitor_plague strikes again.

It's worth noting he didn't mention checking the caps in the PSU too, or the voltages, because they go bad there too --- and can cause further destruction if they cause the voltages to go far out of range. In particular, a bad cap in the PSU standby feedback loop causing the +5VSB to go up is somewhat common. I've seen it at ~6, 7, or even close to 10V in one particularly bad instance. That would certainly damage any mobo connected to it. A common symptom of high 5VSB damage is a machine that (possibly intermittently) doesn't stay in standby after being shut down, or turns itself on immediately upon applying power.

I had forgotten that such an old machine had a full-screen BIOS logo

I believe most if not all of the prebuilts from Compaq, Dell, HP, IBM, etc. had that. Mobos sold standalone had the classic BIOS POST screen, but some had a utility to let you create a custom one.

A desoldering gun is a lifesaver. The Hakko FR301 is a good example, you do have to keep it clean and eventually you will clog a nozzle through laziness, but its easily serviced with good parts availability. There is no need to caveman around with desoldering braid or damaging other components with a heat gun.

For those not in the know: SFF = Small form factor.

It is interesting to see the ESR (Equivalent series resistance) of the capacitors replaced too. This can be more significant than the absolute capacitance.