Can you get into recovery? If so, try wiping the cache partition first to see if that helps.
If that doesn't help, do you have usb debugging enabled? If so,
should be able to use the Nexus 7 toolkit. Just boot your tablet, plug it in your machine, fire up the Nexus 7 toolkit and have it unroot and relock your BL.
You might also want to try and see if you can backup your data partition and your internal storage with the N7 toolkit. If you can do that, then you won't lose any of your data or application settings.
You should also be able to flash it back to stock as well via the toolkit and have it erase the user data.
If usb debugging is NOT enabled, then you might be hosed. You could at least do a factory reset in the main recovery.
Other than that, not much else can probably be done unless you want to open your tablet yourself and ensure all the connections are tight. There might be a lose connection for the digitizer and that's all you would need to do to fix it. Of course, that voids your warranty if you open it yourself. I don't know exactly where the hook up is. I'm sure a quick Google will tell you how to fix this if it's possible.
It definitely sounds like either your digitizer is bad or it's got a lose connection.
Sent from my Nexus 7 using Tapatalk 4
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RAZR HD (unlocked) running Eclipse
32gb Nexus 7