You should make sure you are using the factory wall charger to charge your phone. As Rukbat said, you should let it charge for a few hours at least before trying it. With a Samsung phone, sometimes I have found with my Gnex if I don't have the battery seated just right, it won't power up.
Personally I use a battery only charger and have more than one battery for any phone (with replaceable battery) I own. That way I charge the battery only, switching them when needed and leave that port on the phone for file transfers and hacking. The added benefit of doing this I have found is that my batteries last longer overall and between charges as well.
good luck