I bought a camera today and it won't turn on

It is a nikon D3100, i've charged the battery fully and followed the instructions to the book but as soon as i try to turn it on there's no response.

Make sure the polarities are correct

I would suggest that you contact the Nikon customer support team on 0330 123 0932 (This number is open 9am-5pm Monday to Friday) OR just take it back to where you bought it.

Maybe you didn't charge it?

Last I checked, the batteries in those cameras only fit one way so I doubt you've installed it incorrectly. You may very well have a defective camera. I'd take it back to the place of purchase and ask for a replacement or refund. This shouldn't be a problem if you purchased the camera from an authorized dealer. If you bought it from an unknown, third party, you may be out of luck.