Follow these steps to fix the problem:
Symptom: EOS 7D won't turn on. Battery is charged. Tried several batteries. Battery door closed. CF card compartment door closed.
Diagnosis step one: Is the Lithium battery fresh? Replace and check. (My best bet here!)
Step two: Clean the battery contacts in the battery compartment. In particular the silver one that is closer to the back of the camera. Use a screwdriver and slightly scratch any oxidations off the surface of the lowest, protruding part of the silver contact. After that clean with cotton swab and alcohol. Carefully clean the two copper contacts with cotton swabs and alcohol.
Step three: If it still won't work or the camera fails again shortly afterwards, remove bottom plate and see if one or several screws of the bottom circuit board (towards the handgrip or towards the CF card door) fell out. Happened to my 7D, too. Shaking the camera and tapping with a screwdriver can remove the screw from the innards... Mind the flash capacitor! If none of this helps, you might have to replace the circuit board. Good luck!