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For the last week of so we have had serious issues with our 1 year old google nexus 7 tablet. The behaviour has been:

It starts up, displays the “google” on a dark background, then the animated coloured “X” while the operating system boots up and presents the locked user screen.
We could unlock it and start using it but within 10 seconds it would stop responding and then reboot.

Over and over again, it did not matter what user functions we tried but the absolute time of lockup and reboot varied by quite a lot.
Plugged into power or not, over and over.
At times we got into the settings and turned off wifi, bluetooth, and other features, no change.

After many hours of troubleshooting, research on the net, taking it apart and reseating the battery connection, making sure it was charged fully, we decided to try a factory reset.
That in itself was a hit or miss proposition, what with trying to hold down both the up and down volume buttons and the power button but not knowing which to let go first if at all, how long to hold them, etc, before it would start up in bootloader mode.

Once there we navigated our way to the factory reset setting, confirmed many times and it finally erased and reset.

On the next startup it came up to the initial user setup and did not crash and reboot.
We reentered google account info and it pulled back the local configuration as saved in the google cloud and all in all, all of the local content and configuration was back again. And still no crashes and reboots.
We created a 2nd account, just in case it was a first account corruption issue and it too is working fine.

It is a good thing… I think the 1 year warranty had run out… and we don’t event really remember where it was purchased from in any event.