Am having problems with my Compaq 6720s

Need more info here, you said no display but then said "sometimes the screen goes blank", so is there no display or does it work then goes black? What exactly happens when you turn it on? Does it try to start Windows? When does it stop booting? Can you enter the BIOS setting normally? That's an old system, did you try a new hard drive and a clean Windows setup? Could be a failing motherboard also, or RAM issue.