Have you tried booting in safe mode? If you can run it for long periods in safe mode, it could be a recently installed program that's causing the crashes. Have you installed any anti-virus programs recently?
Have you tried a clean install? You could try that (backup any files you don't want to lose first) and then add just one program at a time to see if there's a particular program that's the culprit.
Other than that, I'd probably find a Toshiba help forum and post the info you provided above and see what they say.
I'm on my second Toshiba. Neither gave me the blue screen, so I can't help you from experience. I'd buy another in a second, but I wish they made a desktop.