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/im...
• if you do have the LTE version, download https://developers.google.com/android/im...
NOTE: Download the last one on the list only, you don't have to download everything.
Follow these instructions to install adb.
Follow these instructions to unlock the booloader from fastboot mode only. Don't do anything else here.
Finally install the large firmware package with these directions using the directions here:
NOTE: Start at "Flashing Factory Images".