Is my iMac done?

After about a hour of usage my imac "stutters"(getting very very slow to the point of minutes of lag when typing) then quite quickly after just stalls with the dreaded beach ball of death. When this first started happening it eventually led to the computer not booting at all. I've reinstalled the OS (snow leopard). It happens with any program from safari to PSE external HD or not. I've brought it in for a check at the genius bar and according to the staffer it did not seem to be a OS X issue(but to be fair he didn't use it for the hour it usually takes for it to be an issue.) I think of it as an issue with overheating just due to the fact that you will get that first hour where it works great?

Any thoughts?

Jim