The dell power connector is held in place by narrow flanges. It is easy to break one side or both and this causes the power connector to move enough to sometimes connect and frequently stop connecting. If the laptop is in warranty, contact Dell tech support. If it is out of warranty, find a take apart instruction that matches your laptop and check to see if the power connector is loose in the case.
Another thing that sometimes happens is the power connector gets damaged when the power cable is pulled out at an angle. There should be a black plastic insulator in the middle of the power connector, the insulator protects the inner contact from shorting out on the barrel of the power cable. The power connector is different from each model, although the pin out is the same; so be careful which power connector you get.