Why won't my screen turn back on?

For starters, my iPad Mini doesn't have a home button and it is cracked. Anyway, I turned on my screen and it pulled up my home screen with all my apps, but it wouldn't pick up my touch. I tried turning off the screen, and it wouldn't go dark. It showed my home screen for 5 seconds, then the screen shut off. It "glitched"on and off 2 times, but then it shut off and it wont turn back on. I tried holding down the lock button and I plugged it into my computer, but nothing is working. It says it is charging on iTunes and it is on 59%, but the device will not turn on. Am I going to have to replace it and/or buy a new one?