I would call Apple ASAP on this one.
My mom purchased an eMac about a year and a half ago. It gave us so many problems we returned it and put the money towards a 17" iMac.
As a Apple Service Manager told us over the phone, "eMacs historically have a lot of problems. You're not the first, or the last."
If I were you, I'd get rid of it and invest in a better computer. eMac's are very unstable at this point.