Try pressing the tiny reset button on the back, and '''then''' try to charge it.
My brand new controller was completely dead. I had it in the charger for hours, then took it out and tried turning it on. Still no life signs.
Then I pushed the reset button on the back with a paperclip, and pushed all the buttons again. Still no luck.
Then I plugged it back in again, and finally the LEDs started flashing.