Just because it happens within the first few minutes does not mean it is not heat related. If there is a contact problem between a heatsink and source it could very well overheat in a few seconds. However that is unlikely after 4 problems on different laptops
Can you start the computer in safe mode? If so, try running the normal startup programs one by one and see if you can recreate the crash.
You could also try looking through this if you haven't already http://en.community.dell.com/forums/t/19325689.aspx
I hope this helps