It does sound like you have a hardware problem creeping up. Possibly the hard drive. If it runs for some period of time you could install a SMART monitoring utility to check condition.
Any number of utils would work. For short-term checkups I tend towards <a href="http://www.sofotex.com/SpeedFan-download_L4655.html">speedfan</a> since it also monitors temperatures.
It would also be worth running Dell's diagnostics overnight. I'm not familiar with their current stuff but you probably have it in the laptop firmware or on one of the install CD's.
Do you notice anything common happening before the crashes? Will it crash just idling or is it only during use or transition (warming up, moving, etc.)?