Hi, there may be at least three issue regarding this symptom.
# The charger / USB cable is not working
# the charging port is broken
# the battery is dead
So how to troubleshoot this problem?
* change to another charger
* change USB cable
* finally if none is working, change the battery. It would cost around USD $20
I've try to use hardware reset / factory reset (press Power button and the Home button simultaneously) but both step fail.
Last option, get a new phone.