Some Power Supplies do crayz things on the primary side when something on the secondary goes wrong.
An amplifier I repaired a few weeks ago, for example, blew both switching-transistors (Push-Pull-Configuration) when the output-cable that normally goes into the speaker touched the case repeatedly.
I was unsure if something else was broken, so I ordered a few transistors more than needed, but it really was just the 2 N-FETs that were blown. The rest of the amp was fine and worked like nothing happened after replacing the FETs.
I'm guessing that the PSU tried to bring the 3,3V-Rail up and started oscillating because the 12V-Rail and 5V-Rail went overvoltage, which the old caps didn't like (excessive ripple current paired with high ESR due to age = Lots of heat).
Try fixing the short on the 3,3V-Line and replace the two filter caps. Old PC PSUs are good if you want to test stuff that needs a bit more power than the standard 31V / 5,1A Lab-PSU can deliver.
Just connect the green wire to a black one and the PSU switches on the moment you flick the power-switch.
Unless it is one of those abominations without a power-switch. Those need to be purged by the cleansing flames of the Emperor