I have the same issue on an Inspirion 550 - now 3 years old.
I have dismantled the whole system.
Only have the power button connected.
The PSU has a green light - the motherboard has a steady yellow light.
Without pushing the power button on I start to hear a clicking sound (not very load) then I see the PSU and the mother board lights flashing with each clicking noise.
Some have the power is not flowing through - inverter - capacitor?
All I did was power off the machine last night as it was running a little slow - would not power on this morning.
Grrrrr - - out of warranty - $200 to upgrade to get a warranty. Is it worth it?
Disappointing that it has bearly lasted 3 years
$500 for a new one.
Cheers