probably damage to the board from using a non-apple charger. the iphone 5 is kind of prissy about that. but hopefully it is just a bad battery or dock connector.
your troubleshooting looks like this:
1.) replace battery
2.) replace dock connector
3.) send out for board repair of charging circuit---which may or may not be feasible depending on whether the charging power ic or the charging logic ic was damaged.
good luck!
jessa