My sister and her boyfriend have been complaining for about a year that their PC (my previous PC, built by myself many years ago) sometimes doesn't boot up: when switching it on, the hardware starts working (hard disks and fans spin up, LED's light up) but nothing appears on the monitor and, apparently, the OS doesn't get loaded either. Pushing the RESET button usually helped but a few weeks ago even this was not enough to make the thing work properly.
The problem is not entirely unlike yours and the reason was very obvious: the (relatively) large, (relatively) high-voltage capacitors on the motherboard were puffed up a bit: their top was not flat but visibly round. (Well, 4 years of pretty much constant usage.) I was brave,
went to the electronics shop, bought capacitors of the same parameters and carefully (!!!) soldered them in place of the old ones. To my extreme surprise, the thing works now. (Except for the PS/2 mouse; probably, the capacitor near its port is not soldered properly, gotta check it when I have some time.)
So, if you suspect the motherboard, check the large capacitors.