Can you boot it up without it plugged in? If not, its definetly a battery fault. Replace the battery imediatly as it could be leaking acid inside of the computer, and if it is, it will eat away at the inside of your computer and your screwed.
At this point I don't think being able to run off battery power is a priority.
The OP came with a problem in not being able to run off AC wall power due to a bad connection at the laptop, not the wall outlet. The first priority is to get the cord or jack repaired so that the laptop will run off AC power.
While their have been some reports of some dangerous batteries, this is not common. I don't think there is any reason to panic about this at this point. If the laptop is going to the shop to check the AC power, the technician can open the battery compartment to check out the battery too, if desired.
If you want to try this yourself, Vickie, just turn over the laptop and remove the battery cover from the backside. Take it out and see if you can see any leaking or corrosion on the battery.
The main thing now is to get your power cord or connector jack repaired so you can run off wall power.
