Well, without seeing the error, it would be difficult to troubleshoot, but what you can do to prevent the computer from rebooting:
1) Click 'Start'
2) Right-click "Computer"
3) Choose 'Properties' from the menu
4) Click 'Advanced System Settings' on the left
5) On the 'Advanced" tab, click the 'Settings' button under "Startup and Recovery"
6) Make sure that under the "System failure" section, the following boxes are set appropriately:
a) "Write an event to the system log" is CHECKED
b) "Automatically restart" is UN-CHECKED
7) Click 'Ok'
8) Click 'Ok' again
9) If it says you need to reboot, reboot
This will prevent the computer from rebooting when it happens so you can get the details from the BSOD, and it should write it to a log.
Once you have that information, we can look for a specific fix.