Hello Deller,
Well Deller, I think you already know what I'm going to say by the sounds of it. It's obvious that the problem lyes somewhere onboard the motherboard, most likely the power jack due to wear and tear. If it's the power jack, you can pay for a new one to be soldered. In some cases, the wear and tear caused by movement of the socket itself can damage the motherboard. In this case, your only option is to replace the motherboard.
There are companies that specialise in Jack Repair such as:
Jack Repair | Laptop Repair Direct
Just to present a slightly cheaper alternative. The power Jack is not the only source of power. Dell Laptops have a docking port at the bottom of the laptop, which you can attach a docking station to. The docking station has it's own power connection.
DELL 0GH051 D/Port Port Replicator for Dell Inspiron and Latitude Series at Laptop Parts World