Computer Shuts off while using Internet Browser.

How about go over your configuration and make sure you are set to create Small Memory dumps. Whichever one you used last time, use a different method this time. Make sure there is a folder named Minidump in C:/Windows.

Have you gone over your wiring real close? And I guess the first question should be are you actually having BSODs? A BSOD looks like this

Attachment 346674

Well, I honestly have no idea why it won't create memory dumps. I'll see if I can find someone who may have some other ideas.

Please run a full scan with your Anti Virus and also please run scans with

Anti-rootkit utility TDSSKiller
Anti-rootkit utility TDSSKiller
ESET online scanner:
Free Virus Scan | Online Virus Scanner from ESET

I hope I'm not being in the way.

I have found that if one uses clean up tool like Ccleaner or others they will remove the dump files.
Also Windows 7 Clean Disk will also remove the dump files.

Then you don't seem to be really getting a Blue Screen of Death, which is why there is no dump file.

Manually create a restore point. It may be your only way back. The link is below then

   Warning

Be sure to create a System Restore point before proceeding further System Restore Point - Create

Driver Verifier - Enable and Disable
Run Driver Verifier for 24 hours or the occurrence of the next crash, whichever is earlier.

   Information

What is Driver Verifier:
It puts stress on the drivers, and tries to make the faulty driver crash the computer. It is designed this way, to attempt to trap the offending driver.

What you will notice:
It will tend to make the computer rather slow and sluggish because the drivers are being stressed.

   Warning

Before enabling DV, make sure you have created a system restore point before enabling Driver Verifier. make a System Restore Point manually before enabling DV.

   Tip

• If you fail to get on the Desktop because of DV, Boot into Advanced Boot Options > Safe mode. Disable DV there. Now boot normally again, and try following the instruction of enabling DV again.
• If you cannot boot in Safe mode, do a System Restore to a point you made earlier.

Let us know the results, with the subsequent crash dumps, if any.

OK, great. Run it for 24 hours of use and do anything you want. Anything that usually makes the computer crash, do it frequently. If it seems a little slow and sluggish, that is normal, don't worry about it. If you get a BSOD upload the Blue Screen of Death (BSOD) Posting Instructions