Nexus 7 2013 screen won't come on. When to give up?

Question

My Nexus 7 2013 is no longer working properly: I cannot get the screen to come on, and I don't see any evidence of back-lighting even in a dark room. I believe the device starts up and shuts down properly because when it's connected to my computer via USB, I can browse the files on the tablet.

On two occasions, I was able to see the boot screen ("Google" logo with an open padlock at the bottom of the screen). The 2nd time it happened, there was an unusual white horizontal line (typically the background is solid black) crossing the screen. That was two days ago; nothing since.

I suspect it's a hardware issue, but I don't know how to test. So I have two questions:

What can I try to fix the problem? I'm open to using ADB, fastboot etc, but need detailed instructions (am noob).

If the problem can't be fixed, how can I safely clear all my info from the device before I dispose of it?

The Nexus is on Android 5.1.1, and is rooted with an unlocked bootloader. The device is also fully charged.

More info:

When I plug the device to my TV's HDMI, the Nexus outputs the Android UI to the television, and the tablet screen can sense my touch (I can navigate the touchscreen, although nothing is displayed on the tablet itself). So if any diagnostic or fix requires me to see what's on screen, it's doable

— BeetleJuice | Sources

Answer

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.

— Ethan Z | Sources

Nexus 7 2013 screen won't come on. When to give up?

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