If you have charged it all the way, and it still fails to try to get past the Nexus logo, it could be a battery issue.
To test this issue, see if you can get into "Fastboot Mode" and see how long it stays there.
• First, you have to turn off your device – perform a complete shut down sequence, don’t just reboot your tablet (press Power button and select “power off” or press and hold power key for a few seconds).
• Then, in order to enter fastboot mode on your Nexus 9 you need to press Power, Volume Up and Home buttons at the same time.
• Keep pressing these keys until fastboot mode is being displayed on your device.
• The START option should be listed in the upper part of your screen.
Now, if it goes at least 2 hours without powering off (you may need to touch the Vol buttons once in a while to make sure the tablet doesn't restart or simply goes into power save), you have a software issue.
To resolve a software issue, please be aware that your data likely will be erased.
• if you don't have LTE on the tablet, download https://developers.google.com/android/images#volantis
• if you do have the LTE version, download https://developers.google.com/android/images#volantisg
NOTE: Download the last one on the list only, you don't have to download everything.
Follow these instructions to install adb.
https://forum.xda-developers.com/showthread.php?t=2588979
Follow these instructions to unlock the booloader from fastboot mode only. Don't do anything else here.
http://forum.xda-developers.com/showthread.php?t=2507905
Finally install the large firmware package with these directions using the directions here:
https://forum.xda-developers.com/google-nexus-5/general/tutorial-how-to-flash-factory-image-t2513701
NOTE: Start at "Flashing Factory Images".