1. Are you sure there's power to the outlet? (It's amazing how many people turn a switch off, the switch controls the outlet, then they expect the phone to charge from the outlet.)
2. Have you regularly been discharging the battery past the 40% point before recharging? If so, by now the battery could be dead. (It will have to be replaced.) Lithium batteries are not deep-discharge batteries.
3. Have you tried a known-good charger and cord (one that does charge a phone)?