Do you not see the small blue letters "Recovery Booting" (upper left corner) when you attempt to boot in recovery mode? Which Samsung logo are you seeing? I guess I'm wondering if you're attempting recovery the correct way. Make sure to press and hold the Volume up, Home button... and then press the Power button. The Power button must be pressed and held last.
You might try using Kies or Smart switch to reflash the phone. I've always used odin and have never used Kies or Smart switch so I can't tell you how to do it... but here's a Kies video by Rootjunky...
01-07-2017 02:12 PM