BleepingComputer.com: Reboots when trying to install New O/S

Hello, I've posted about a similar issue before, but here's what's going on.
I've had my laptop, a Dell Vostro 1500 since January 2008, in the past 2 months I've noticed that I can't remove the A/C Power adapter without the computer rebooting, even though the battery is fully charged. If I keep the cord unplugged the laptop boots fine off of battery, and if I plug the cord IN there's no problem.
So I decided to install Linux, to see if that solved the problem. First, I tried a LiveCD. After a couple minutes the laptop rebooted. Figuring I had a bum burn I tried again with an older LiveCD that I knew worked. It also rebooted.
So just earlier I decided that perhaps a Windows 7 RC install might work. Well, it didn't. It does the same thing, after a few minutes running it reboots.
I run Windows XP currently. I haven't seen anything odd in the logs. The Dell Diagnostic CD reports everything as fine (and oddly enough if you pull the power cord in the Diag. CD it doesn't reboot) and XP doesn't have the problems of randomly rebooting.
Please, I would like to know if anyone has any ideas of what is wrong or at least if anyone else has had this problem.
Thank you much,
-Sweet