I had the same problem with my Lenovo Vibe P1.
What I did was I pressed down the volume keys + power button and as soon as the screen lights up, leave the power button but still hold the volume keys down. It would enter another screen whereby you'd see options like "reboot, install update package, wipe user data" and "power off". Instead of going for a factory reset, I selected "install update package" and just clicked on the yes option that follows on the next screen(it reads something like install from internal memory).
The update of course failed because I didn't have an update.zip package in my phone. Once that is done, go back to the menu and select power off. Switch it back on after a few seconds and see if that works for you It worked for me Unlike what's said in the previous replies, I couldn't enter safe mode at all. There was no such option for me so I just tried working my way round it
You can try starting it up in "Safe Mode" and see if it will load. While you get limited access in that mode, if it will start up then you know there is something on the device you need to remove. Virus, malware, bad app, etc. If it won't start up, even in that mode, then it is probably a hardware issue.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.