Can you follow the instructions here, Troubleshoot Firefox crashes (closing or quitting unexpectedly) and post back with some crash IDs? We might be able to figure out what the problem is with those.

I don't get to see the crash reporter as my computer shuts down and restarts

Here's instructions for getting crash IDs even if you can't open Firefox: You can't open Firefox because it crashes at startup even in Safe Mode:

1. Click the Windows Start button, and select Run... on Windows 2000/XP or press Windows Key + R on Windows Vista/7.
2. Type in "%APPDATA%\Mozilla\Firefox\Crash Reports\submitted" including the quotation marks and click OK.
3. In the resulting folder will be a text file for each crash report you have submitted. Using the View menu, arrange them by date to find out which is the newest file; and double-click on it to open it.
4. Copy and paste the recent crash IDs into this page.

No records since 01-20-2011

Can you try creating a new profile and see if the issue still happens? Instructions here - Profile Manager - Create, remove or switch Firefox profiles.

I'll give it a try

Downloaded full FF 10 and reinstalled. Created new profile. So far so good. I will let you know. Thanks

If this continues to work for you, you may want to recover bookmarks and other things from the old profile. Instruction for that are here: Recover important data from an old profile.

Seems to be working now. Thanks for your reply

Hmm. Thought I was in the clear. Now I'm back to square one. It starts all over. Switching to IE untill you have this figured out.