Must constantly restart when on the Net

My husband loves to play the games on the Net at places like iwin.com where they have slots etc. It seems that after playing for a while the computer runs very slowly and he must shut the computer completely off for a few seconds. When he restartsthe computer is good for another 20 to 30 minutes. This is the second computer he’s had that has this problem. He has a PIII-600EB with 256 mb PC-100 SDRAM, Intel mb. This only seems to happen when on these game pages. I’ve tried using many programs like FreeMem Pro, etc. but nothing has worked. Any suggestions?