Yes, I'm using the load from the first post. Plus a diode so as I said there's no excuse for the spikes. The load itself might be oscillating as well but still there's no excuse.
It is probably the caps - as I said it is rather old and it's been really, REALLY used. That P3 went strong from something like 2001 to 2011 and it's been used all day long, sometimes it was left in bed on while watching a movie (lucky it didn't start a fire). I had to replace the panel as the hinges and back-light were gone, also the whole palm rest/touch-pad as they were really, really worn out but still survived. It's been retired as defective but in fact only the power connector from the motherboard is flaky, otherwise it still works.
Too bad for the power supply, I really liked it how small it is. I'm pretty sure it's only the caps but I don't think I'll be able to put it back if I crack it open.