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.