For whatever it's worth, I had a sort of similar issue to what you've described when I got my current PC - power came on, fans ran, but no beeps, no LEDs (besides the motherboard's power light), no disk activity, no signal to the monitor. My case was a little different in that I was able to get it to boot if I powered down, turned it off at the power supply switch and turned it off at the wall socket, waited a couple minutes, then turned it all back on again... but I had to do that every time I booted up or I'd get the previously described results.
In the end it turned out to be some sort of compatibility issue between my motherboard and my RAM. Both were fine on their own and not faulty per se, but it seemed the motherboard (or maybe the BIOS, I vaguely remember talk that it would be fixed in a future update) couldn't handle the RAM at its specified speed (3200). Since I was able to get it to boot under specific conditions, I was able to get into the BIOS and reduce the RAM speed a bit (I think to 2800), which resolved the problem entirely.
I've no clue how likely it is that you have the same issue, but figured I'd share in case it gives you some other avenues to explore.