I had the same problem as well. After trying several different solutions posted on other sites, new power supply, new battery, tapping on the logo, etc., I found the real solution. There is a severe design failure happening here.
Dell wants us to buy replacement batteries and power supplies from them, not 3rd party manufacturers. For the power supplies, they send an identification signal over the center pin of the power supply. If it does not identify itself correctly as a Dell, then you get the annoying message at startup and the battery will not charge. Well the technology was initially designed several years ago to work over about a 3-6 inch transmission path. Now they are using it over the 2-3 feet path of the power cord. This requires the transmission path to be broken.
This is why some of the fixes posted on other sites work for a while, but they will eventually stop working. The bottom line is that the power input connector on the computer is breaking down over time. This should not be happening, this should have been designed properly and tested properly, but it obviously was not by all of the problems out there.
Being an electrical engineer, I went and bought a new power input board on Ebay for about 25 bucks. I then took on the very difficult task of replacing it. This should not be tried by people that are not tech savvy. There is a very good chance that your computer will not work again. You have to remove every screw in the base, take off the keyboard, all of the plastic, remove several connectors, then remember how it all goes back together.
The good news is that replacing the power board does fix the problem. I would buy the board off of ebay, then take it to a local shop and have it installed.
This is my last Dell computer. I was a lifetime Dell user, but this design failure is completely unacceptable. It is a huge issue within the computing community. They sold thousands of these computers with this faulty design and do not own up to the problem. This problem should not start showing up after 6 months.
Good Luck!!!!!
Karl
September 2010