Thank you guys. I've downloaded BurnIn to test a system that sometimes it won't turn on at all (or just turns on with nothing on screen).
At first I thought it was the RAM, replaced the RAM and it worked. Tested the RAM with MemTest+ for around 6 hours and no errors. This morning I turned the system on to get nothing on screen... so it shouldn't be the RAM. Replaced the PSU and the system worked fine.
To be honest I've never did any stress tests on systems before, but I think it would be a good idea to make it a habit. BurnIn did a 15 minute test on the RAM, CPU, Hard Disk and Graphics. It passed with no errors. Do you think that after this test, the PSU is good enough to handle the every day usage ? (due to the tests performed).
Naturally, I'll be working on this machine for some more time just to make sure. I will also turn it off during the night and turn it back on in the morning to see if it turns on fine.