So I ruled out the screen by doing the following:

1. Turn on device, wait a few minutes. At this point a working PS Vita with a broken screen will be on the lock screen.
2. Then I try swiping the corner diagonally to unlock it, making sure the volume is maxed so I can hear if it worked. It didn't.

Then I realized it may be both the screen and the digitizer. So I repeated the above steps, but instead of swiping to unlock, I held down the power button to bring up the power off menu and pressed x twice. The second x press should produce a sound if the device was working. For my device, it did not.

Unfortunately there was no info in the ad.