Update: I checked the voltage outputs and found something interesting:
On the good power supply, we get a near perfect 12v across +12v and GND, and about 3.5v across the LED.
However, across +5v and -5v we seem to be getting nearly *10 volts*.
I checked the 78M05 regulator and got a perfect 5 volts - until it started wobbling and shot flames at me. It no longer gives any voltage now.
The fault was probably somewhere else in the circuit, since the regulator seemed to be okay before it killed itself.
After the 78M05 blew, we get nothing across either rail - both 0 volts.
I checked the transformer and it is perfectly on the dot - it was definitely on the DC side.
My main question now is whether or not the machines will work anymore. Should I attach them to a modern PC supply, since they have +5, +12, -5, and GND rails? Would that be safe to test the machines with?
EDIT1: The 78M05 is back? It shot a lot of sparks last time, but it's giving me 5 volts again, but the output of the supply is still 10v and 11.8v.
Could I simply replace the capacitors or is there something bigger happening here?
EDIT2: Attached a 12v PC fan to the 12 volt rail and it ran with no problems. Put it on the 5 volt rail expecting it to be at a similar speed but it dropped severely after a few seconds and fluctuated quite a bit as if there was a lot of noise in the output. My oscilloscope is currently dead (sweep tubes got water damaged), so I can't really check for this at the moment. Measured across the 5 volt rail with the fan attached and it seemed to be at around 5 volts - it might just be some open circuit voltage, but I don't really know how to tell. Maybe the fan is just asking too much of the supply (12v .13A)?
I've got no capacitor tester right now, otherwise I'd check the electrolytics.
EDIT3: I checked the bad supply - the 12 volt rail is a little low at 10 volts and the 5 volt rail is giving me nearly 20 volts open circuit! The regulator is giving out 10v on this one so it's definitely bad, but could any part of this computer have survived this? Closed circuit it's far less than 5 volts - about 3.7 volts or so with the fan attached.
I should stop testing these, they're making me less and less hopeful of the computer's survival.