Shoutbox

I had this kind of symptom for a while:
If I did a warm boot (restarting a computer), my computer would restart fine
If I powered on my computer after being shut down for a while, my computer would refuse to start.
No BIOS screen/option at all, no hard drive's light blinking. Just a blank screen.

So to get around it, I would have to wait for a few minutes and then press the reset button on my PC.
BUT... if I simply did "sleep" my PC, my computer would start fine although I had left it shut down for days.

Now, this is worse.
I have been noticing that my waiting time was longer whenever I powered on my computer after shutting it down.
And finally, last night and this morning, my PC refused to start although I've let it run for 2 hours.

Any idea what the problem could be?
I've had the computer for 2 years and it always ran fine (my usual practice was shutting down my PC).
Suddenly I had the first symptom described above about 6 months ago.

Thanks in advance.