Default [Q] Nexus 10 stuck - read only? I can't update or change anything.

Hey guys,

I'm experiencing a weird problem with a Nexus 10 that was gifted to me. For some reason the Nexus 10 can't receive any updates and reverts to it's last state after a reboot. That probably doesn't make sense so here's an example:

I turn on the Nexus 10. I change the language in the settings. I connect to wireless. I install apps. When I reboot the nexus 10 has no history these changes were made.

Wiping/factory reset from Recovery does nothing. I can select the option but when I turn the tablet back on there is still a completely configured profile with personal data present.

It's currently stuck on 4.2.2. When I try to install the OTA update the installer downloads, the tablet reboots, then no record of the install is seen.

Finally, I've tried to flash Google factory images via ADB and fastboot. But, I can't complete the install because the bootloader doesn't remain unlocked after a reboot so the install never finishes. It seems to me the tablet memory is stuck in a state of read-only.

It seems to me the tablet is stuck on Read-Only somehow... does anyone know what else I can do? I've never experienced this problem before. Most of my research indicates an eMMC problem?

Thanks!