i've had EXACLTY the same problem you are describing about a year ago. i spent a long time on the phone with them. they sent me a different power adapter and that did not help. i sent in the laptop to their service department and the problem was resolved. it is still running great a year later.
I have a couple year old Gateway 600ygr (1.8ghz pentium 4) that seems to be on the downslide. It has worked great up until a few weeks ago when it started to lock up when disk cleanup was run, but only when it was hot and when it was running off ac power, not battery. I've noticed that the fan is kicking on alot more and staying on alot longer than it used too. Is there any solution to this or am I dealing with a lost cause?