It sounds like what first happened to me, and the problem was a bit of both actually. I had received the wrong AC adaptor (as did some of the pre-orderers who received the first shipment) so the charging pin was technically the wrong size and it was hit or miss whether it would actually charge the battery. I also happened to have (either as a coincidence, or as a result of running it for a couple of weeks with the wrong AC adaptor) a defective battery that wouldn't fully charge. When I received the replacement battery and AC adaptor, things were fine.
So if it's the problem I had, it's that you might have the wrong size charging connection. If you search earlier threads, you'll probably see people talk about the different millimeter measurements of the connector (check around the first couple of weeks of April). Then, try measuring the length of your AC tip to see whether maybe you just got one of the old chargers by mistake.
Is your machine relatively new? I think it took a week or maybe even two for me to notice the problem. The good news is, if that's the problem, it's a quick fix, and the unit would be fine. I know it was a relief to me knowing the unit itself was OK.