It sounds like its a power jack issue. Yup after all you've done thats pretty much what Id bet the money on.
if your handy and trust yourself, order a matching one online and swap them out. but be carefull, my toshiba's just had a plug that I pulled and replaced, in some cases they're soldered right to the power board.
If you don't want to repair yourself, check if its still under warranty, if it is deal with dell, if not find a local authorized dell repair shop (for the love of god not best buy or a big chain, find a small repair shop). it will probably run you about 60-100 for the repair, but they will most likely use a better part than was stock and it wont corrode as fast.