I have a friend’s iPhone 3G that does not and has not at any time had the Wi-Fi connection available. It is greyed out with "No Wi-Fi". I have restored it a dozen times to no end. He wants me to put his phone on Straight Talk, but to do so I need to open a mobileconfig file which is usually emailed, or edit the APN with a tethering app through Cydia. I have installed the apps into Cydia through Cyder II, but Cydia still cannot load them without internet. Help me please, I've been hunting for and trying work-arounds for hours.
I have heard many times of wifi greyed out, and generally it was right after updating their iOS with a new version. No amount of DFU seemed to fix it, and I think it is because the issue was with the firmware killing the iPhone's wifi.
I am fairly certain Apple repairs these types of problems, you might even call them and see if they will replace it as their update possibly caused it.
For the second piece, If you are trying to get a network connection without wifi, prepare for some fun. It looks like you will need to run some sort of proxy service on your computer, modify some plists, and then run a few commands. The first link has some more mac os x specific stuff, but they are both worth a read.
I think Wi-Fi disappears because of 3G. I noticed that when I open 3G, Wi-Fi stops working.