Dell Xps 17
My laptop showed a low battery signal and then stopped working. I was using the ac adapter at the time because the battery has been dead for a while. I bought a new battery but didn't change the problem. Is the problem the AC adapter?
Sounds like it.
If the laptop is plugged in, it should run no matter what the state of the battery is--you can even remove the battery while the computer is plugged in, normally.
Also, on most laptops at least, there should be some visual confirmation that the laptop is getting power--the battery or power light may come on when the machine is plugged in and off, or there can be an LED near the power jack. If nothing at all happens when you plug the laptop in, it's probably your AC adapter.
I had a recent Dell laptop power adapter go bad after a while--something came loose in the cord. You should be able to pick up a generic replacement (make sure you get one that meets or exceeds the wattage of the adapter that came with your unit and offers the right tips). I bought a Kensington unit at Best Buy, and it came with the added benefit of a powered USB port to charge my mp3 player. Handy. It was about $100, you can probably find these online for less. Dell also offers replacements but they take longer to ship.
If a new adapter doesn't solve your problem you have a bad motherboard or power jack, which will require either replacement under warranty or a bit of soldering by a repair shop. Try the AC adapter first. If that doesn't work and you're still under warranty, call Dell. If you're no longer under warranty, take it to a repair shop.