I have disassembled the thing and followed the instructions of the service manual and even checked 3/4 of all the fuses with a volt meter to see if the motherbord was fried. They all seemed OK. I forgot to mention that at that time, the computer would not even start at all ( no fan noise). So I finally reassembled it without the hard drive and it boots up with a fan sound.. A little bit better... But it shuts down as explained above.
Now, I have read a couple of posts about thermal paste on this site and thought that maybe the cpu is overheating because the thermal paste is dried up. Could an old cracked thermal paste cause this kind of problem?