Last night, sitting quietly in front of this computer:
Bang (serious bang, not just phut). All the magic smoke escaping.

Oh *bother*.
Hang on - other computer is off.

Both CPUs are on the same UPS. Did the UPS die? No - seems to be OK.
Hit the power button on the other box. Seems ok until - Primary slave disk won't mount.

*bother*

but Linux should come up without that. Lilo ... 01 01 01 ... that's bad. *extra bother*. Leave it running a couple of hours. Phew - disk has spun up. System up! Was afraid I was up for a new box.
So:
One power supply and this one is up.
One replacement disk to go in the other box at the weekend.
And they now each have their own UPS.