I have the same problem. I have a 1 week old new Toshiba A100-237 Laptop. I can run other adobe applications such as After Effects 7 and photoshop perfectly. However, when I open up premiere pro 2.0, I get the infamous blue screen of doom seconds before the first premiere pro menu that lets you create new projects or open existing ones is displayed. The computer then forcibly restarts. I’ve tried clean re-installs of premiere pro, but nothing seems to work.
Since you have had the same problem with another Toshiba laptop of similar build, maybe some settings in the laptops needs to be tweaked in order to get them to run?