hackinghardwaremacbook pro
Here's a project I've been desiring for a while. Hopefully this is not too off topic.
I'd like to take a MacBook Air, remove the case, screen, battery, speakers, keyboard, basically everything. I want to have just a motherboard and hsf running osx and usable via vnc over wifi for ultraportable number crunching power.
What problems do you think I might run into? Is there any reason the air won't boot if the aforementioned components are removed?
DVI (DVI = Digital Visual Interface) does never carry sound, it's visual only. Buying a Mini Displayport to HDMI does not help you out either because it's not supported for your Macbook Air.
Here's the list of laptop models that support audio pass-through via MDP
MacBook Air 11" Model 3,1
MacBook Air 11" Model 4,1
MacBook Air 11" Model 5,1
MacBook Air 13" Model 3,2
MacBook Air 13" Model 4,2
MacBook Air 13" Model 5,2
MacBook 13" Model 7,1
MacBook Pro 13" Model 7,1
MacBook Pro 13" Model 8,1
MacBook Pro 13" Model 9,2
MacBook Pro 15" Model 6,2
MacBook Pro 15" Model 8,2
MacBook Pro 15" Model 9,1
MacBook Pro 15" Model 10,1
MacBook Pro 17" Model 6,1
MacBook Pro 17" Model 8,3
and any version later
You can use the Apple MiniDisplayPort to DVI adapter with a cable like this: 
and a separate jack audio cable.
At the risk of sounding obvious, something inside broke. If you are the handy type and have the tools you could open it up following the directions for your model on iFixit.com or take it to an Apple store (or other Apple dealer who does repairs) and see what they say.
Also do not power on a laptop with something rattling around in it after you dropped it. It could make the problem worse.
Best Answer
Bart Reardon is trying to convert a broken MBA into a "computer in a keyboard". The project looks a bit stuck right now, but from one photo you can see he has removed (some? all?) components from the Mobo. Perhaps you could ask him if the thing still works if everything is removed. I’d be interested to know!