I was notified that there was a system update, but when I applied it the tablet was still on the older version of Jelly Bean. I've even done a factory reset and tried again, but no luck. Are there any logs that I can look at to track down the problem?
Before updating make full backup of your data.
For update using computer you just need to flash system partition using fastboot
fastboot flash system system.img, where system img available at
image-nakasi-jop40c.zip available inside
nakasi-jop40c-factory-6aabb391.tgz, what you can download from Google Nexus factory images page.
Using scripts from tgz archive will erase your data without prompt!
Dont't flash data, even as you got bootloop (it can be, if you has applications, incompartible with new version of firmware).