This has been a chicken or egg problem I've run into several times. The classic computer won't start symptom with the telltale p.s.fan that that just quivers. Ninety plus % chance there's a dead supply and the user has the computer overloaded with peripherals that tax a stock supply. In most all cases, a new supply is all it takes to bring it back to life.
Other times it's been a bad board or peripheral. Sometimes noticeable bulging caps/leakage on a 7+ y/o board. Something I'd take a shot at changing out and ESR'ing suspected others if it were my personal machine. These are obvious or easily traced, but occasionally you get a weird one like I did a few months ago.
Seven y/o machine whith the above classic fan twitch, 200W stock supply with 3 IDE drives, a racehorse video card, obsolete, analog tv tuner card, original modem, not to mention choked with dust and under the CPU heatsink packed with dog hair and dust mat. This supply must have been gasping to keep up. The user reports that it's been taking several tries to get the computer to turn on recently. Now it's dead.
Pull all cards, dust/blow out the machine, unhook everything except board video and add new 480W supply. All is well, add back only video card and drives one at a time, no problems. Two weeks later, computer is dead. pull supply and have a go/no go tester/load, won't start and dead.
Swap supply and all is good again. About a month later the same. Put in another new one and ask them to run it w/ primary drive and board video for a while. Kid's at school, so no gaming and they only use it on the net 24/7. Less then a few days I get a frantic call that smoke is pouring out of the supply. Sure enough, and electrolyte leaking everywhere. Obviously a board problem that took out several supplies I have to eat.
So you know the scenario. You can't be sure in this case intially which was the problem and not much you can do otherwise. Board shows no visible traces of overheating, bad caps, all fans working, and a supply large enough for the job. Home audit shows a perfectly working UPS/Surge supressor and small multipurpose scanner/printer working perfectly on the same ups. Transients on the power line are out of the question. This leaves the board the major suspect.
For supply side testing, I have both a field go/no go load and led idiot box and a more elaborate dynamic LCD metered, load tester to check supplies independently in the shop.
Does anyone know of any diagnostic ATX connector interface that can be put between a good supply and a board that can flag excessive power demands and perhaps help isolating the board? This would be nice tool in the days of aging desktops.