Why my phone not turning on?

Press power button, volume up and down button together and wait for few minutes, and it will appear with something and you have to do cancel, and it will reboot your phone

I agree with @oldturkey03, this kind of issue is usually caused by a bad battery. However, in the meantime, have you tried to boot to recovery mode? To do so, when the device is turned off, press and hold the volume up, home, and power buttons until the Samsung logo appears, at which point you should release them. From there, a couple things could happen:

1) If the phone goes into recovery mode properly and remains there without boot looping, this could be a software issue. Try clearing your cache. It should be one of the options that will pop up once recovery mode loads, will read something along the lines of “clear cache”. If clearing the cache does not work in this circumstance, and you have a recent backup of the phone and/or do not need the data on the device, it may be worth it to try and factory reset through recovery mode.

2) If the phone does not boot into recovery mode or does but restarts itself without you telling it to do so, your phone will need hardware repair/replacement. You could order a battery and since the model’s battery appears to be user-replaceable, swap it out to see if that fixes the issue.

If neither course of action works, it will need further diagnostic. Depending on your level of phone repair experience, at this point it may be better to bring it to a professional for a diagnostic.