Computer dead

Yesterday my son was on the internet and working fine. When he was finished I performed a logoff (Windows 2000) and logged onto another user account (on local machine of course). After 5 minutes the screen went black and the computer would not do anything. I rebooted and logged in again but after 5 minutes samething happened. I tried one more time and this time the computer wouldn’t even boot up. The indicator lights are on but nothing is happening. I didn’t get any beep codes either. After waiting an hour or so I booted up again and was able to log on but after 5 minutes the scenario started all over again. Thoughts?