Laptop Shutting Off

I need some help here and want to use everyone here as a sounding board, maybe we can come up with something I missed (I hope).

The laptop in question is a Dell XPS M1730 Laptop. I was told it was shutting off at random on the person. They have to use the power button to turn the machine back on and it goes through a normal Windows startup at that point (just in case I have checked and sleep mode and hibernation are completely off since it's always plugged in). Only when you put the lid down does sleep mode activate and that works normally.

Anyways, it was becoming a bit more frequent recently, happening up to twice a day. The laptop is located in the same place, on the same plug 95% off the time and it's been shutting off there only. It's always plugged in.

The battery is pretty much ready for replacement, but I tested pulling the power and the battery does kick in and will give you at least 5 minutes+ still. Plus there are always warnings when the battery is low, it shouldn't just shut off instantly.

The first thing I thought was overheating. I had the user check the temperatures while in normal use and I've also been running it steady under normal conditions and under heavy loads at times for hours on end (since I've now gotten a hold of it). Temperatures seem normal, nothing too high or out of the ordinary. I've been monitoring it for a couple days.

I should also note it has not shut off once on me in this entire time either and I've been running it fairly steady.

Even though I don't think it's at all related, I have tested for Viruses and ran memtest to check the memory and nothing came up.

I also had a look in Event Viewer and checked for any mini dump log files from Windows. Nothing there either at all. Aside from one event talking about Windows being shut down improperly.

Does anyone have any ideas as to what could be causing the laptop to shut off on its own?