I was wondering will I get a compensate if the screen was not working the entire flight from London to LA through the British airlines? I did report the issue.
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.