Hi,
When you plug in your charger does the phone show that it is charging?
If so, let it charge for a while, then see if you can start the phone with the ''charger still connected''.
If it does start, shut down and then see if you can fully charge the battery. If it doesn't then the battery is faulty and needs to be replaced.
If the phone does not charge with the charger connected, try another charger.
If it does then your charger is faulty.
If it still doesn't charge with a different charger then the charging circuit in the phone or the battery is faulty