charger - Laptop not charging when connected to mains outlet

I've had this laptop for a few weeks now, it's a Sony Vaio.

I went to charge it a few days ago and plugged in the power cable, but it's not charging. The battery icon in the Windows taskbar to the bottom right says it's plugged in and charging, but the charge level never goes above 2%. I have checked and I don't have a hcarging switch on the laptop anywhere, so it should be charging.

If I unplug the cable, the laptop runs out of power within 30 seconds or so, further fueling my thought that it's a faulty battery.

Anyone have any bright ideas? If this doesn't get fixed I'll just ring up Sony and get them to send me a replacement battery or something.

Thanks.