Some general advice:
- Make sure nothing else is connected to the laptop at all, no USB, no VGA, no nothing. Just making sure...
- See if your laptop has the latest BIOS, and if it does not, flash it to the latest BIOS version.
As far as troubleshooting minidumps, the official Microsoft reference seems to be:
http://support.microsoft.com/kb/315271
debugging tools must be downloaded from:
http://www.microsoft.com/whdc/DevTools/Debugging/default.mspx
I also found a reference to WhoCrashed which, given the minidump as input, will supposedly tell you which driver is most likely responsible for it. I have not used this myself but it looks reputable. Might be easier..