Hi.
Do you try different chargers?
Try this - be sure battery is charged. Try to enter "Download mode" or "Android System Recovery menu" (press and hold VloumeUP+Home+Power or VolumeDown+Home+Power).
If you can't do this, you have a hardware problem, the phone must be opened checking.
If you can, then may be you have a software problem. You can tray to reset it from the Recovery menu or flash it with Odin from Download mode. But you will lost your data.
Regards.