The iMac has an internal AirPort Extreme card. Attached to this card is two antennae cables. See the image for Step 10 in the following iFixIt link:

If the AirPort card is not properly installed or is faulty, it would not show up in the OS X System Profiler.

Try the following, in order, checking for Internet access after each step, until resolved: 1. If the modem has a reset switch, use it to reset the modem. Wait at least 5-10 minutes for the modem to initialize. 2. Remove power from the modem. If it has a backup battery, remove this as well. Wait 5-10 minutes. Replace the battery, and add power back to the modem. 3. Perform a complete power recycle of your network components as follows: <b>Modem/Router Power Recycling - Quick</b> o Power-off the modem, AEBS, & computer(s); Wait at least 5 minutes. o Power-on the modem; Wait at least 5 minutes. o Power-on the AEBS; Wait at least 5 minutes. o Power-on the computer(s) If this fails to get the modem to "recognize" the Internet router, then try the "Full" version. <b>Modem/Router Power ReCycling - Full</b> o Power-off the modem, AEBS, & computer(s). (Wait at least 30 minutes. If possible, leave the modem off overnight.) o Power-on the modem; Wait at least 15 minutes. o Power-on the AEBS; Wait at least 5 minutes. o P...

Try the following: 1. Delete Preferred Network(s) o System Preferences > Network > AirPort > Advanced > AirPort tab o Under "Preferred Networks," delete the network(s) you regularly use from the list. 2. Delete AirPort Keychain Entries o Launch the "Keychain Access" application located in Applications/Utilties. o Click on the "Kind" filter at the top, and look for any "AirPort network password" entries...and delete them. o Restart, or log out then back in. 3. Add Preferred Network(s) o System Preferences > Network > AirPort > Advanced > AirPort tab o Add the preferred network(s) using the "+" button. o Restart or log out then back in.