I see there is a scr crowbar circuit on the 5v output, and since it is an old computer from the attic, I am kind of suspecting this to be linked, I also assume that the PSU works with no or light load, or it will with new caps.
Old electrolytic capacitors might have partially dried out during attic time, so just booting up and doing small stuff gives the impression everything is fine, but when pushing it with a complex program the total current consumption loads the tired caps so much that the ripple trips the crowbar circuit, and byebye fuse
If I read the pictures right then the lone to220 in the middle of the secondary section is the SCR crowbar, and if it is triggered in the same way as you example schematic then as soon as the 5v reaches the trip voltage the scr shorts the 5v output.
I would check all caps for value and ESR, if this is not possible then replace the caps in the secondary side of the PSU and also replace the caps on the main computer board, if it is hard to replace the caps, then as minimum reinforce as meny as possible of the power caps on the main CPU board with a new good quality low ESR cap in parallel
Well that was my best guess based on the available information .