First, please stop YELLING. Typing in all caps is looked at like yelling... Thanks.
Second I would NOT reccomend that you lap the CPU core. It is very small on the Celeron2 and would be very easy to screw up. Also, I do not know how thick the plate is...
Third, what Heatsink are you using? If you are using the stock HSF, then go and get a better one like the Alpha PEP66T or something. Are you using any thermal paste between the CPU and the HSF? If not you REALLY should be, and I reccomend Arctic Silver.
Fourth, you should have some way of monitoring CPU temps, heat could be causing your instability. Get some way of monitoring it...