did it ever restart for u when u were unpluged from the net? if your on dial up then u wouldnt be connected most the time, but im guessing your on cable/dsl? u use wifi?
note- im not realy headed anywere specific with these questions.. but was just thinking, if there is nothing rong with that comp, maybe it could just be some hack messing with u? especially if u use wifi without wep enabled?