Selling Broken Kindle Fire... My info?

I stepped on and broke the screen on my kindle a while back. I don't want it anymore (for various reasons), but because the screen doesn't turn on I can't factory reset (I'm guessing). Should I be worried that the person I sell it to fixes the screen and then has access to my email, etc.?

Or do the accounts time out after a certain amount of inactivity and require you to sign in again? It's been about 6 months since I've used it.

I guess I could just change my gmail password, but don't really want to..