How much does it cost to repair MacBook Air fan?

I've had my MacBook Air for three years, and a couple of weeks ago my roommate dropped it and dented its corner. There were no problems for awhile, but now the fan is running extremely loudly (it sounds like a blowdryer) and the computer is getting extremely hot. I ran a diagnostic test and it said: 4M0T/4/40000002: Exhaust -269, which I take to mean the fan is broken.

I'm wondering whether it is worth it to bring the computer in for a repair when it won't be covered by Apple Care (because the damage the result of dropping the computer) or just investing the money to repair it in a new computer? I would normally bring it into the Genius Bar but the wait times in London are over a week and I desperately need a computer during exam time.

Thank you for any advice!