You reported Crash ID

bp-5dc7626b-e8e6-4529-b7e8-d0bd42120129 
bp-96fdd636-ab9e-4ef1-9dda-e0ea42120129 
bp-4a87c657-7294-4914-b960-1aea92120129 
bp-118c5fe5-bf47-48cd-8081-fd79e2120129

All of them have the same crash signature, e.g.,

https://crash-stats.mozilla.com/report/index/118c5fe5-bf47-48cd-8081-fd79e2120129
Firefox 9.0.1 Crash Report [@ RtlpTpWorkCallback ]
Related bugs 
647366 NEW Firefox Crash [@ RtlpTpWorkCallback ]
688743 RESOLVED DUPLICATE FF shuts down when 'some' pages are opened. If it doesn't shut down, a new session of FF opens with multiple 'didn't load' tabs

Did you try the suggestions in the Troubleshoot Firefox crashes (closing or quitting unexpectedly) article? See if Firefox runs without crashing when you start up in Firefox Diagnose Firefox issues using Troubleshoot Mode (which is different than Windows Safe Mode):

1. Hold down the SHIFT key while starting Firefox
2. In the Firefox Safe Mode window, click "Continue in Safe Mode".

If Firefox doesn't crash in Firefox Safe Mode then it's probably an extension causing the crashes (in which case you should disable all extensions in the Firefox Add-ons Manager) or it's a video device issue (in which case you can disable hardware acceleration in Firefox). See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems for steps you should take.

Note: If Firefox runs fine in Windows Safe Mode then it's probably something that runs in Windows normal mode that is interfering with Firefox ... for example, see http://kb.mozillazine.org/Firefox_crashes#Other_installed_software for a partial list. See also Troubleshoot Firefox issues caused by malware.

It still crashes in Firefox Safe Mode. So does that mean there's a problem with my computer and not Firefox?

You said in your original post that your computer restarts randomly but that everything seems to work OK in Windows Safe Mode. Something that runs in Windows normal mode that doesn't start up in Windows Safe Mode is causing the problem with your computer, which could be a malware or other software.

P.S. It might even be a graphics device or driver issue, since your "more system info" says, under Graphics, that Firefox hardware acceleration is Blocked for your graphics card because of unresolved driver issues. and Windows Safe Mode loads a basic driver. (See this windowsBBS thread and this sevenforums thread for examples.)

I think your best bet would be to visit a forum specializing in Windows issues, such as http://www.windowsbbs.com/ http://www.sevenforums.com or http://www.bleepingcomputer.com/forums/