Not starting up

take it back defective battery

what charger are you using?
if usb
try wall charger as usb wont charge when in restore mode unless the phone is on

Try a car charger. If the car charger works, then it is either
A) Your power outlet
B) Your wall charger Power Supply unit
C) The phone connector on your wall charger.

If it doesn't work on the car charger, then it is most likely your phone charging system or the connection for charging on your phone. Either way, you will most likely need a new phone. Sorry.

charging problem

try with a new battery your could have give up

OK CHANGE UR BATTERIE IT WILL ON OK RATE ME

You may try to do factory reset of your phone (save your data first!!):
'Home' > 'Settings' > 'SD card & phone storage,' then select 'Factory data reset.'

take the phone back and have it replaced.

First of all (change your 1.charger 2.battery 3.battery jack then there will be a problem of Power I.C because the battery jack is connected to power I.C then change it.....That's all.

your phone hardware might be dead , there is no way u can start it , u need to go for a service of your phone and they will flash the entire hardware and reinstall the software