Hi, I'm new...

[Scott Quinn]

 I'd see if there was some way to put a voltmeter on the power coming in. If the computer draws more than the supply can put out, the supply voltage
will drop.

I've never seen a resistor short- I've had several caps short out on me, though. It's evident when that happens, though - there's usually a bang and puff of smoke.
I'd expect the smoke if anything shorted out, the components usually aren't rated highly enough to survive a dead short. Usually it's some passive that goes, though.