If it only turns on when plugged in then first suspect is the battery, replace it and charge it outside the phone so you know it is fully charged.
If that doesn't allow it to switch on then you can try flashing the same firmware you already had, with odin, but you may end up losing all your data if you need to factory reset.
A custom recovery, like philz, would allow you to backup data on the internal sd.
You will need to read and follow the guides in general forum as some of these steps can brick your phone if you get it wrong.
Note: This quote doesn't automatically apply to everyone, decide for yourself if it might apply to you.
Originally Posted by justruss
What has this place become?
It's essentially a few people graciously answering the same repeating of immature, lazy, demanding questions from the masses.
Nobody searches. Nobody reads the first posts or titles of threads. Nobody even looks at posts a couple above their own.