[Q] My Nexus 7 got stuck on X screen

Assuming you are already rooted and have a custom recovery and ROM on your internal storage you could try dirty flashing a ROM over it in an attempt to boot.. Other than that idk.

Sent from my Galaxy S4 using Tapatalk

If you didn't do anything to the ROM then the probability is that something has become corrupted. Its a problem we are beginning to see a lot of recently. I guess it may be time to start looking at why this happens. Anyway in terms of your data the best I can suggest is if you can get into fastboot mode power + vol down then you may be able to use the command adb pull sdcard I've never tried it but theoretically you should get a dump of all data on the "sdcard" which on the N7 will be the internal storage. Today's buzz word (phrase) is automated backup.

Programming is a race between engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning.