My Sony DSC - W320 camera won't turn on?

I've had it for about about 4 months now. I took the battery out to fully charge it, popped it back in the camera but it won't turn on. No matter how many times I've pressed the power button, nothing happens.

The battery works fine because when I put it in the charger (which came with the camera) the light comes on (on the charger).
There's been no water damage and I haven't dropped it.
Please help!