Is there a red light?
If so, here's a link that might help: https://gbatemp.net/threads/zte-maven-is-not-turning-on-right-but-it-flashed-a-red-light.437486/
You might also check out this video, though it just describes an issue similar to what it sounds like is happening to you: https://www.youtube.com/watch?v=IQQmdJXmzKs
Useful comments:
"hold the screen down and press the power button really hard." -powder_HfK
"The only thing I've figured out that consistently gets around this issue is to remove the battery, plug in the charger and wait for the display to come to life. You should see the android figure come up and it should cycle repeatedly. Put the battery back in. You'll probably see the warning about the battery being extremely low. Power the unit off and then on normally. It then behaves fine for a day or two, or a week, then starts doing it again. I suspect that the battery just needs to be replaced." -twsbbl
Good luck!