I've recently encountered a Dell Latitude C640 at work that has a boot up problem. The notebook's CAPS LED would flash 10 times followed by the power getting cut off. Putting aside the fact that this is a really old notebook that's in a pretty sorry state, the solution to this little dilemma turned out to be simple: RAM.
Simply open up the rather large panel on the bottom of the notebook to gain access to the memory modules. Proceed to remove all memory modules, then reinsert them properly. After that, the notebook should boot up normally and you're on your way.