So, no device shows at all on the left hand like (besides the DVD/CD drive)?
Try running System Profiler, under Serial ATA (SATA). Under the list of information about the drive (assuming there IS any), check the SMART status. If the status is "About to Fail" or "Fail", you'll have replace the hard drive.
If it's OK, it still should show up in Disk Utility at least as a device. If it does get that far, you should be able to select volume and run the Repair Disk previously mentioned.
Otherwise, it's sounding like time to pay a visit to an Apple Store or, if you are comfortable with the internals, you could open the back and check the seating of the drive's cable connectors. Remember, this is a MacBook Air and things are REALLY tightly laid out in there - it's going to take some patients and skill to gently move sensitive cables around. Is this an original or Late 2008 model? The hard drive cable connector opens slightly differently between the two. (Risky business if you aren't qualified, experience wise.) Also, it's a "if you broke it, you pay for it" policy on self-service under warranty. Just have to weight the chance of an unseated cable versus a possible long trip to an Apple Store or days without while they service it for you. It's here I'll say my "I disavow all knowledge of this procedure and this post will self-destruct in 10 seconds.........." Suffice it to say anything you do inside is at your own risk.
It pretty hard to do remote surgery though this interface, but it could be setup on a one-one basis. Maybe MR's working on something - haven't heard of it. iChat iSight and the counterpart at the other machine should do it. Leopard's built-in screen sharing is worth the prices of admission just on its own. Of course, if it's your only machine, that won't help much unless it's a software problem.
Hope you find it's something simple. Night: sleep now.