In my experience, the power jack on the Inspiron range and Dell laptops in general does seem to work itself loose from the motherboard. I have repaired a number of them over the years, company ones and for friends and family. Sometimes it just needs re-soldering, sometimes a new jack is needed (they only cost a couple of pounds on e-bay).
There are still local electrical repair/TV repair shops about that may do it for you for at a decent price. Specialist laptop repair places tend to charge around the £100 mark so probably not economic.
Ask among your friends, they may know someone who can solder to a high enough standard. Its not for the faint hearted though, there is very little space around the jack and other components come right up to it. Someone who says they can solder isn't always actually capable of working cleanly on a laptop circuit board. I've spent hours repairing a board that someone else tried to put a new power jack into.