Will British Airways compensate if my entertainment screen was defective for an entire flight? [duplicate]

Maybe, but almost certainly not in cash, and not if you don't follow up.

If you send a feedback form from the website, describe the issue, note that you reported it and the crew was unable to fix the issue, you will likely get a small token of compensation like frequent flyer miles, a duty free shopping voucher or a flight voucher. (A better airline would have given this on the spot, but this is British Airways, not Singapore Airlines...). You're not legally owed anything though, so be polite, factual and brief.

Doubtful. You bought a plane ticket, not a ticket to a theater. On a long flight, you could argue that lack of food was a hardship. But lack of entertainment??

What airline ?

You'll probably get (received much later) a voucher of some sorts to buy from the flight store (online shopping).

That's what I got when that happened on a British Airways flight from London to Montréal.

I lost them, it wasn't that much in money anyway.