This is the kind of behavior you get when the PSU is going into overcurrent protection because it's plugged into a short. If they repaired the PSU, presumably they tested it was working before they sent it back. That suggests to me the problem is somewhere else in the machine.
If it still shuts down with the graphics and drives removed, I would start by looking at the -12v rails on the mainboard. A shorted tantalum capacitor can hide here since the whole -12v load doesn't normally draw enough current to cause a catastrophic breakdown of the capacitor (explosion/fire) like you would get on the +5 or +12v rails, but will still cause the PSU to shut down. Measure the resistance between the -12v PSU pins on the mainboard and ground. The load should be less than an amp (>12 ohms). If it's anything under 10 ohms, there's likely a problem. I'm willing to bet you'll find it's under 1 ohm (e.g. a full short).
If it still shuts down with the graphics and drives removed, I would start by looking at the -12v rails on the mainboard. A shorted tantalum capacitor can hide here since the whole -12v load doesn't normally draw enough current to cause a catastrophic breakdown of the capacitor (explosion/fire) like you would get on the +5 or +12v rails, but will still cause the PSU to shut down. Measure the resistance between the -12v PSU pins on the mainboard and ground. The load should be less than an amp (>12 ohms). If it's anything under 10 ohms, there's likely a problem. I'm willing to bet you'll find it's under 1 ohm (e.g. a full short).