Laptop keeps turning off?

So you're saying the laptop will turn off if running on the AC, but works ok when running off the battery? How odd. Sounds really unstable, a lot like this Dell desktop I'm troubleshooting. In my case, this particular motherboard is known to have issues, probably from bad capacitors (swelling/leaking). It may be out of your control and I'm sure it's well out of warranty by now. :( Might be time to upgrade to a new laptop.