Can a battery be so dead it won't charge?
A lithium polymer battery has internal circuitry that is intended to prevent it from becoming fully discharged, and electrically isolates the battery from its external contacts when its charge falls below a certain amount. However, even after that occurs its tiny internal resistance causes its state of charge to continue to diminish, just slower than it would if an external load were present. This internal resistance increases with age.
Unlike other types of rechargeable batteries, a Li-po battery that has reached this completely discharged state becomes damaged and cannot be resurrected.