Random shut down, replaced power supply, problem still present

I have an Intel iMac, 17" 1.83 GHz.

It was intermittently losing power (turns off just like it had been unplugged) about three years ago, took it to an Apple repair shop, they said something about bad capacitors and replaced the power supply. It started doing the same thing again a couple of months ago. It is no longer our main machine (my wife let me build a Core i3 MacPro), so I put it off until I had time to look at it myself. Bad capacitor on the power supply (the 1000µF capacitor at the end of the line of four, right next to the power connector to the logic board). I replaced it with the same type of power supply (Model: API4ST03, P/N: 614-0378). Still intermittently losing power.

What next?