Make sure you have the right model of phone (Not saying you dont, but pull out the battery and be sure it says Model Z796C) and the android versions for all of the ones I have are 4.1.2. You need an internet connection in order for towelroot to run, current version is 3 @ towelroot.com.
It helps to wait about 30 seconds before running root checker. If that still doesn't do it, reboot your phone and try again because I had problems about 30% of the time with towelroot.
EDIT: There's ONE other possibility, and this affected one of the phones I rooted because it kept popping up with google play store errors and the screen timeout wouldn't set any higher than default. Reboot into recovery (adb reboot recovery) then do a complete system wipe and restore. Then install the apk's and try again.