I found a post on the Inspiron site and I have been having a very similar problem with a Precision M2400. That forum indicated an Intel chipset update will fix a monitor shutdown and recovery error? The failure mode I am having with an external monitor is the same. Today I upgraded my Video driver to Driver version 332.21
This version and my previous version (331.82) work fine with external monitors. However as soon as I open up the laptop and switch to the standard laptop screen I will get a BSOD within minutes no matter what application I am running. I also have updated the Bios to Version 28.
I am even running multiple monitors and it operates fine as a desktop PC...unfortunately it will not operate in laptop mode. Once it goes into BSOD mode it becomes a continual reboot to-do loop.
For others in this nightmare...I also found I had to disable sleep mode. On the control pannel settings I have set sleep to never. I just need to remember to hit the sleep button on my keyboard. Going into sleep mode was causing a BSOD in desktop operation on version 331.82. I have not tried turning sleep back on yet.