Out of curiosity, is the isight working OK? Both the bluetooth and the isight share the same cable from the logic board to the top edge of the display assembly under the glass. If the isight is also not working then it is more likely to be a problem with the cable. In the best of all worlds the cable can sometimes come unseated in the logic board and can simply be reseated.
This may be too obvious an answer for you but here goes: The SIM (subscriber identification module) is a small chip/card that identifies you uniquely on the network. It is accessible on the top edge of the phone between the on off button and the headphone jack. There is a tiny hole just big enough for a paperclip to enter and you remove the SIM card by pushing gently in with a paperclip and a plastic frame containing the SIM card will pop out. check that: a) there is a SIM card b) it is seated properly in the device- ie it is seated in the frame properly. If reseating the SIM doesn't work then I would suggest fining someone you can borrow a working SIM from or go to a store and do that--this way you will know if it is the SIM or the phone. If none of this helps, then the problem goes deeper and I'm afraid I don't have further suggestions at this point.
Damaged LVDS cables can be replaced-- but as one responder pointed out it is not a part that is normally sold separately. You most likely place to find a replacement is by buying a display assembly that is non working and salvage the cable. In order to replace the LVDS cable you need to: a) Take the display assembly off of the rest of the MacBook b) remove the glass from the display-- can be done but extremely hard to do so without breaking it so possible you will have to fork over another $70 to replace c) unscrew the existing LCD d) swap cables on back of LCD and re-route new cable through metal frame of display assembly e) screw LCD back in, replace glass A few tips: 1) always test the LCD before replacing glass-- if there is a problem with the cable or connection you want to find it then, not after you have put glass back on. 2) Remember that the problem can be on the logic board and not the screen-- meaning you can have a logic board that works with external monitor and not the internal screen-- but...
Alas, this is more common than you think! The most obvious choices of having apple repair it or purchasing an new logic board are both very expensive-- representing a huge percentage of full replacement cost. One alternative that has not yet been mentioned is that there are a few people who specialize in repairing logic boards, and do so typically for about $250 to $300. Go to eBay and search "macbook logic board repair". These guys clean them, try to identify what chips have been damaged, replace chips if possible and so forth. Thanks to eBay's feedback system, you can know that these are not scams and many other people have had success with a particular repair shop. I sent out a 15" unibody just before Christmas and its repaired and on its way back now. Lastly-- if repairing is not your thing-- remember that you can still get a surprisingly good amount of cash for your liquid damaged laptop on eBay-- probably more than you think!
Keep in mind that as mentioned above not just any SSD drive will do. If you search eBay you will find many SSD drives but note that many are 2.5 inch drives designed to replace the typical laptop hard drive. The Macbook air original hard drives are 1.8 inch drives (ie not as thick) More importantly the connectors and connection method must be the same in order to perform a simple swap as you desire. For A1237 the original Air version the connector is a ZIF (Zero Insertion Force) connector and the connection is PATA. For the A1304, the connector is a LIF (Low Insertion Force) and the connection is SATA. There are not many drives that work. One is Runcore Another is Photofast. It would be a good idea to review this thread that discusses compatibility of SSD with macbook air. Hope that helps.