I plugged my headphones into my laptop and it worked fine but when I removed them the speakers wouldn't play. I tried...

There could be a number of things wrong with your laptop to cause this, it will either be a software or a hardware issue. If you feel capable you can take it apart and check that everything is plugged in right and try again. If that doesn't help you should probably take it in to be looked at.

The best course of action would probably be to take it to an electronics shop and have them look at it, but given that it has such a short charge life it is most likely time to get a new one. You can find a replacement guide for the battery here.