I have a Nexus 9 running Android 7.1.1, and the home button, recent button, all notifications, and the top pull-down menu all stopped working.
The home and recent buttons respond to being tapped in that the animation that indicates I tapped them runs (the gray circle expands out from the button), but nothing happens. I can open the top pull-down menu, but it always says that there are no notifications, and I can't pull the menu down further to expand the icons.
I have about 15 GB out of about 30 GB available, and memory usage is listed at 1.6 GB out of 1.8 GB. I've tried restarting the device multiple times.
If I remember correctly, I accidentally drained the battery before this happened, but I can't recall if the device was simply powered off. When I powered up the device, the PIN prompt buttons caused the device to vibrate, even though I had had previously had that setting turned off. I restarted the device, and that setting turned back off. Double-tapping to wake up the device doesn't work consistently.