Laptop plugged lights turn on but no power

For the last couple days I've noticed that even while my laptop was plugged into the ac adapter and the lights which indicate that it is plugged in were on, the battery indicator would sometimes show that it was not charging. After a few wiggles it would eventually start working just fine. Tonight I was using my laptop while it wasn't plugged in and after leaving it for a bit I came back and it had shut off. I assumed that the battery died so I connected the ac adapter but now my laptop wont start. The lights which indicate that the ac adapter is connected are lit as if it were charging but nothing happens. It's acting as if the battery is completely dead and I'm trying to start it without the ac adapter. Any ideas on what the problem could be? I would assume that I have a problem with the ac adapter but like I said...the lights which indicate that it's connected are lit and they were also lit when the battery indicator showed that it was not charging.