samsung galaxy note 3 neo won't turn on

First of all, what happens exactly when you try to turn it on?

The initial turn on process works like this:

1. Hold power button 3-5 seconds

2. White samsung logo appears and transitions to next logo

3. Animated samsung / android boot logo

4. Phone boots up successfully showing the lock screen / home screen

If anything else happens in those steps please post it here, e.g on step 2 the white logo text just disappears and reappears again to signify it is trying to turn on again.

or phone just turns off and does similar to what is done in step 2.

Have you tried replacing the battery? That's one of the things that first come into my mind if the phone just instant shuts off after it turns on and boots up or shows the white samsung logo text and shuts off.

If it's doing it at the animated samsung logo text then it could be a software related issue.