That doesn't sound good. I fear the motherboard could possibly be going out. But that's a dirty word in tech support especially with laptops so lets stay optimistic. You gotta start with a full diagnostic though. Test your ram, processor, memory, and hard drive. If one of these devices are bad, then replace it end of story. If all tests good then at least you aren't looking at spending a lot of $$ for parts or a new computer. Let us know.
Btw I think Dell is pretty good about including diagnostic utility CDs with their new computers. If you cant find it, I would visit the website and look for it there.