One thing to keep in mind when having your tablet serviced by someone else is that irregardless of what you paid for it, there's still that labor charge involved. Some places will evaluate an ailing device for free hoping to make up the loss in charging for the actual repair, some places charge a flat rate, and some places charge by the hour. But bottom line is they're going to make money off of you either way.
If the screen did fail, you wouldn't be seeing that error message flashing on it. You wouldn't be seeing anything. When a tablet doesn't boot up properly that's usually an indication the operating system has become corrupted in some way. You were able to a Factory Reset, but note that a Factory Reset only wipes the user data partition clean, it does not affect the operating system in any way, nor does it do anything to any of the other partitions dedicated to the system -- so a problematic operating system remains a problem, Factory Reset or not. It's not that you shouldn't have done a Factory Reset either, that would be part of trying to diagnose the problem. (*** And hopefully you had previously set up a backup solution so all your saved data and files can be restored when your tablet is up and running again.)
If the operating system needs to be restored, that's a process referred to flashing the ROM. Flashing a ROM is basically the same reinstalling the operating system on a PC. It's replacing the existing operating system with a clean one, essentially returning the device back to its original state as when you started it up the for the first time. But unlike a computer install Disc, a ROM is unique and runs on only the device it was created for. Each model has its own ROM, they are not interchangeable with each other. So you need to flash your tablet with just its matching ROM. Luckily there are multiple sources for verified, stock, Samsung ROMs. The Internet being what it is there are also a lot garbage everywhere so you do need to be very judicious about what you install on your tablet.
What is the specific model of your Tab 2 8.0? It should be something similar to SM-T817
