We've owned three Dell laptops over the last decade, and all three sufferend this problem. It's probably going to be a connection that's gone bad on the motherboard. If you Google, you'll see that's an epidemic with them. The only solution when we dealt with it is to replace the motherboard. You can get one relatively cheap off of eBay, and they're not hard to switch out.
Here's the rub though (the next one anyway), it's the same motherboard make and model, every single one we replaced went bad the same way again after a while.
Solution? I stopped buying Dell laptops. Result? Eh, different manufacturer, different problems. The machine I'm on is dying with power-related problems too. Going to have to replace it at some point, and don't have a clue where I'll go. A few people are pointing me towards MacBook Pros.
If you call their customer server, tell them I want my $50!