My MB Air went to Apple a couple of times for fixes just before the warranty went out, then the warranty ended and within a week the sound died. Typical! I tried new OS install to no avail. Then I researched on iFixit and saw people had similar problems with audio cable so I decided to give it a go.
It was very straightforward with the detailed photograph step by step instructions. When I removed the old cable I could clearly see that it had been crushed at the bend destroying the tiny wires inside - probably by the Apple repair guys that replaced the drive.
Don't rush! It took almost exactly the 45 minutes that was suggested so take care and it will fix the problem.