Computer shuts down while playing games!

[CTdrummerguy]

Having frustrating computer issues right now. My laptop keeps shutting down when I play video games. It seems to be somewhat random, but only while playing games.
When the laptop shuts down, its instant, despite being plugged in and having the battery in place. There is no log in the event veiwer, only one upon startup that says it appears to have shut down incorrectly.
Here's the facts:
-Hardware
Toshiba Satellite P755-S5261 64-bit
Windows 7 Home Premium, SP1
Intel i3-2310M 2.10GHz (no OC)
6 GB Ram
Nvidia GeForce GT 540M w/ 1GB DDR3
-New power supply (issue happened before too)
-New internal fan
-Already taken it apart and replaced the thermal paste and cleaned out the heatsinks
-Drivers currently up to date
-Ran a HDD test. Had a few bad clusters, but they were able to be fixed.
-Tried with a different HDD (assumed it was the beginning stages of disk failure) and different OS, Same result. After about 10 mins of play, it shut down.
-Ran a RAM diagnostic twice (6 passes +cache), no problems
-Baseline temps
CPU core 0/1- 39°C
GPU temp- about +5° ambient temp.
-Ran several torture test/benchmarks.
Unigine Heaven Benchmark
GPU temp- 54°C (Peak over 5 consecutive runs)
GPU Load (Core)- 99%
GPU memory Controller- 39-55%
GPU memory- 52.8%

Prime95
Torture Test
CPU core 0- 70-71°C@ 100% Load
CPU core 1- 70-72°C@ 100% Load

Figured I'd try both Uniqine Heaven and Prime95 together (since games tend to work the CPU and GPU simultaneously). Ran for 15+ mins, no shutdowns.
GPU temp (Peak)- 60°C
GPU Load (Core)- 99% Peak
GPU memory Controller- 36-55%
GPU memory- 53.8%
CPU core 0 temp- 82°C (Peak) @100% load
CPU core 1 temp- 81°C (Peak) @100% load

It seems like the CPU temps are a little high, but I can't replicate the shutdown, even at 100% load.
Don't really know where to go from here. Anybody have any ideas? Help!

Edit: was able to take readings right before shutdown.
GPU temp: 57°C
CPU core temps: 68/67°C

 

[Akutalji]

My brother had the exact same issue on his Sager laptop from a while back (2nd Gen i5, GTX600M 2GB, 16GB RAM). He did almost as much as you did, in terms of troubleshooting (swapped HDD, RAM, tested both, stress tests for CPU/GPU/combined). After several phone calls with Sager's customer support, they finally decide to honor the warranty (they kept telling him nothing was wrong). Two weeks later, a phone call from them, reporting a short in the motherboard, "not visible, but there" they said. Probably a fracture in one of the layers in the board.

One new board later (yes, they installed a new board, not a whole swap. Hardware IDs/SN matched) and it never experienced the issue ever again.

Warranty it. Or, if it's out of warranty, it will most likely need a new board. You essentially troubleshooted it to the MOBO already.

Edit: Cleared things up a bit.