Wifi no hardware installed

First, determine if the problem is hardware or software related. I would expect it to be a hardware issue, but boot from a clean OS installation just to be sure.

If you've confirmed it is a hardware issue, first reseat the flex cable connection on both sides (logic board and WiFi card). Perhaps used compressed air to ensure the connections are clean. If that does not solve the problem, I'd replace the cable just because it is an inexpensive part. In my experience, if the system does not recognize the WiFi card, the card itself is usually the culprit, but WiFi flex cables on some models (including your early MacBook Air) can be problematic. While not completely unheard of, it is rare for the WiFi connector on the logic board to fail.