Shutdown & reboot/hang

Sounds like a hardware problem. Please try uploading/attaching this:

Upload Dump Files:
Please go to C:\Windows\Minidump and zip up the contents of the folder. Then upload/attach the .zip file with your next post.
Left click on the first minidump file.
Hold down the "Shift" key and left click on the last minidump file.
Right click on the blue highlighted area and select "Send to"
Select "Compressed (zipped) folder" and note where the folder is saved.
Upload that .zip file with your next post.

If you have issues with "Access Denied" errors, try copying the files to your desktop and zipping them up from there. If it still won't let you zip them up, post back for further advice.

If you don't have anything in that folder, please check in C:\Windows for a file named MEMORY.DMP. If you find it, zip it up and upload it to a free file hosting service (not RapidShare as the analysts usually can't download from it) - then post the link to it.
Then, follow the directions here to set your system for Minidumps (much smaller than the MEMORY.DMP file): Set MiniDump

Also, try these free diagnostics:

H/W Diagnostics:
Please start by running these bootable hardware diagnostics:
Memory Diagnostics (read the details at the link)
HD Diagnostic (read the details at the link)

Also, please run one of these free, independent online malware scans to ensure that your current protection hasn't been compromised: Malware (read the details at the link)

*****
Additional tests for certain specific circumstances:
Try this free video stress test: FurMark: Graphics Card Stability and Stress Test, OpenGL Benchmark and GPU Temperature | oZone3D.Net

FurMark Setup:
- If you have more than one GPU, select Multi-GPU during setup
- In the Run mode box, select "Stability Test" and "Log GPU Temperature"
Click "Go" to start the test
- Run the test until the GPU temperature maxes out - or until you start having problems (whichever comes first).
- Click "Quit" to exit