Try entering Download Mode to see if the device is bricked, otherwise it is either a faulty battery, charging jack, charger or dead hardware (mainboard).
To enter download mode: Press and hold: Volume Down button + Home Button + Power button
If the device goes to download mode, it probably means the device is not charging for some reason. Verify the charger is known good and working and if it is, the phone needs servicing.
I am unsure if the download mode key combo is correct for the SGS 4G model, but that is the key combo for the Galaxy S series.