The power connector on the dells is notoriously bad. On my laptop:
- it isn't a problem with the connector coming away from the board, as all the joints are good.
- it isn't a problem with the powersupply, as known good power supplies also don't work (and the little green light on the power supply goes on)
It looks like it's something internal in the socket on the motherboard. Mine is working at the moment because I have a little scrap of paper pushed into the hole[1] which puts just enough pressure on something that it connects. It's not going to last forever, and when it finally fails
- i can't find a replacement part
- you can't just use a 2 way dc adapter, as the dell supplies have a cunning middle pin which lets the motherboard know what the adapter is rated for.
So I'm not sure what I'm going to put in it's place.
*Update - just found a replacement, which I think is also right for yours (assuming that it is your power socket):
http://www.laptopjacks.com/view_part.php?id=DL111500(but check the ridiculous price

)
[1] I'm assuming your connector is like mine, in that it has a circular channel that the plug fits into. If so, I put a 3mm strip of paper into the channel, with one end sticking out, so that when the plug went in, the paper was on the outside of it. I can try and write a better description if that doesn't make sense...