Nexus 7 2013 screen won't come on. When to give up?
This is hardware damage. Your local electronics repair shop can probably replace the screen if you would like. The manufacturer is a possibility too, but it will be expensive. 

As for recovering data, most of what you will need to save is stored to the SD card (emulated most of the time), and you said you could view the internal storage. Save whatever you feel you want (always downloads folder and DCIM). Most other data is saved to the cloud by Google and can be automatically imported into a new device.

If you were able to access ADB, you can take a full system backup using the backup command. When it requests access, tap the bottom left corner of the screen after unlocking the screen as if it worked correctly. It's okay if this doesn't work, what you can already access should be sufficient. 

You're lucky. Most people cannot access the internal storage when this occurs.

As for wiping the device, you have access to the screen! Navigate to Settings-> Privacy -> Factory Reset. This will delete all data on the phone.