Right, I'll start off by saying that I'm quite tech-dumb and while this site has helped me quite a bit with putting everything in a straightforward way, I'm still blocked when it comes to most things gadgety. So if this problem is obvious or has been asked about before, sorry.

My macbook has currently started having an issue and I'm wondering if it's just a battery problem or something else. I've had this macbook for a couple of years now and the only real issue that I've had was having to replace the power adapter. Now for the past week or so the power adapter and my battery have been doing some strange things. Sometimes, depending on how it's feeling, it seems, the adapter will just turn itself off, as will the lights on the battery. It'll have stopped recharging entirely and I'll have to move around my laptop and/or the power adapter. And if that doesn't work, I'll generally flip it over, take out the battery and place it back in. Sometimes it works, sometimes it doesn't. Eventually, the adapter might decide to turn on again, depending on how the laptop is placed, but one slight jar and it'll turn off again.

Anyone have any idea what the problem might be?

It sounds like just bad contact with the magsafe board. It is possible it could be something more major such as the logic board. But if the machine isn't actually turning off it isn't that big of a deal. Like if you take out your battery and leave it out. If the machine shuts off, you know its something with either the adapter or the magsafe board.