Hello,
I cleaned my pc's fan and now it
failed to turn on. It just turn on
with 4 beeps and than show a
message that the computer was
shutdown previously due to a
thermal event (overheating). But
when I touch the CPU fan and
the CPU, it's not really hot! What
should I do ?

If you can determine the model of hte motherboard, you should be able to visit their website (from another computer of course) and look up the beep codes. This should provide you with more information about the condition that is preventing hte computer from booting.

If you received a message during POST about a thermal event, I would open the case and verify that you have properly secured the fans. If you removed the fans at any time, you may need to re-apply the thermal paste between the chip(s) and your fan(s).

Does the fan still kick in when you turn your PC on ? did you know the heat sink when you were cleaning the fan ?

If the fan doesn't kick in when you power-up check it's connections (but be as gentle as a butterfly).