Hi,
The LED light on the back of my iphone 4 won't turn off. Even when I turn it off the light still stays on.
I did a restore and the light stayed on the whole way through it.

Does anyone know what is wrong with it or how to fix it?

Sounds Like A Backlight issue, take it back to apple, they may off sold you a faulty iphone, or try to put it in dfu mode, and restore from there see wat happens