JD, I think it's either the charger or power port. You can try resoldering the charger cables; if that doesn't work, try another charger on the laptop. If that still doesn't work, then your power port is broken and needs to be re-soldered or replaced.
Sam, too bad. I've never had a problem with any Dell, and I've owned 5 so far. I guess it depends on the models as well. I might've been lucky, or you might've been unlucky.
Now my laptop's dead. Dangit. I have no money so I can't send in my laptop to be fixed or buy a new charger, so if this resoldering doesn't work I'm *Can'tSayThisOnTV*ed.