I received roughly $780 in Unemployment Benefits. I was issued a "W2" for the amount I earned.

However, after the W2 was printed, I received a court order to pay back all money I received on Unemployment. Would I have to claim this W2 on my taxes, even though I have to pay it back and basically didn't earn anything

Claim the unemployment compensation on Line #19 of Form 1040.

Then claim the same income as a negative figure (-$780) on Line #21 of Form 1040. Attach a copy of the court order to your return with a statement explaining why you claimed, then unclaimed the unemployment compensation.

This way, you account for the $780 without paying taxes on the money you returned.