Dropped iPad, now odd screen and button behavior.

iPad was working perfectly, then it was dropped. The drop cracked the digitizer but not the LCD panel. Now the iPad does weird things...

The power button no longer works at all. Pressing it to turn on the iPad does nothing; holding it down to turn off the iPad does nothing; holding it and the home button does not make the expected screen capture.

With the battery completely drained, I can plug it into a charger and it turns on. The Apple logo shows up, it boots normally, and I get the normal "swipe to unlock" screen. However, touch no longer seems to work at all.

If I leave the iPad alone it goes into lock mode, as expected. But when I press the home button to wake it up it behaves differently. Normally, pressing home will instantly bring up the "swipe to unlock" screen but now when I press the home button there's about a one second delay, then the clock -- ONLY the clock, nothing else -- appears on the tablet. (The large clock on the "swipe to unlock" screen, I mean, not the little clock up in the corner.) After a few seconds the clock disappears, as if the iPad were going into lock mode again.

My thoughts...

Maybe the drop ripped the power button flex cable, killed the digitizer, and ever-so-slightly shifted the video cable. Think I'm on the right track here?

I allowed the iPad to completely discharge, then plugged it back into an AC charger (not computer). When it booted back up everything was back to normal -- power button worked, home button worked, screen properly displaying images, etc. Very weird.