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The first and most obvious thing to check is that your charger is working perfectly. If you can, try a different charger or wall outlet. Maybe also try to charge your phone by USB via computer too.
Remove and check the contacts of your battery and make sure it isn't damaged. If it isn't, reseat it back in the unit and put the back on.
If none of that works, then see if you can borrow a different battery from a friend. If not, make a trip to the store you bought the phone from and tell them the issue. Ask to borrow a new battery from them and try it. If none of that works, it's time for a replacement.