Rooted my phone now it won't turn on
My number one advice for people that are new to rooting, flashing etc. is, read at least 5 times before you do it. One-click-root Apps are almost a thing of the past nowadays because manufacturers are stepping up their game with securing their phones.

In your case, that means that you would have to reflash the stock ROM (I doubt that everything is still in tact after you tried to root it) and root then root it properly, for both of which you would need a working PC. Also, you will loose all the data that's on your phone.

For reinstalling the stock ROM, you'll first need to download a few things:

Drivers for your phone: http://downloadcenter.samsung.com/content/SW/201306/20130610184736640/SAMSUNG_USB_Driver_for_Mobile_Phones_v1.5.25.0-retail.exe

Odin: http://odindownload.com/

Stock firmware: https://www.sammobile.com/ (I can't link this to you directly since I don't know your model number, just click on firmware and search for your phone)

Install the drivers, unpack the firmware, connect your phone via USB, put it in download mode (turn it off and hold volume down, home and power at the same time) and start odin. On the right, you'll find many buttons named "Modem", "PDA" and so on. Click on the buttons and select the corresponding file in the firmware folder that you extracted earlier (For "PDA" select a file called "PDA" + extension etc). After all buttons have the corresponding path behind them (only leave those out which you don't have a respective file for, differs in some firmwares), click start. 

Now your phone should be running stock Android again.
For rooting your phone, you need to download:

TWRP: https://dl.twrp.me/core33g/twrp-3.1.0-0-core33g.img.tar.html

SuperSu: https://download.chainfire.eu/696/SuperSU/

Open up Odin again (after connecting your phone and putting it into download mode), click on "PDA" and open the twrp file you just downloaded, then press start.

Disconnect your phone and restart it holding down volume up, home and power at the same time. You should see TWRP come up. Now connect your phone again and copy the SuperSu zip you downloaded earlier to your phone. Next, on your phone go to "Install" and select the SuperSu zip, then swipe to confirm. After that, click "Reboot System now" and when your phone booted, you should be rooted.

Good luck :D