it's a known design issue with dell laptops!
Dell laptops have a little chip in the PSU and another in the laptop that "talk" to each other, the idea being the laptop knows it has the correct PSU connected and it's able to supply enough power for the laptop. the problem arises when one of 3 things happens.
1) the Power socket on the laptop becomes loose and disrupts the communication between laptop and PSU
2) the PSU cable starts to break, again increasing resistance in the data lines and disrupting comms between the laptop and psu
3) the Chip physically dies at either end.
Number 2 is the most common, and the only practical fix for it is to obtain another PSU from Dell. as it's a well known problem stick to your guns with Dell and insist that they replace it free of charge.