Hmmm...if I understand you correctly, the "gadget" you are talking about *is* the airport extreme card. It is a card that is added to the main system board of the iMac to enable it to connect to wireless networks. It looks like this:
Hopefully that works. If it didn't, go to images.google.com and type in "Airport Extreme Card" and you'll see a picture of what it looks like. It is located in a port on the motherboard inside your computer -- underneath the plastic casing.
If you were to sell it, you would DEFINITELY need to take the card out and include it -- people want the card, not the CD so much. Also what CD do you mean? If it's the one that says MacOS 10.3.x (where x is whatever number, maybe 5 or 6 on what shipped on your computer?), then you should keep that, not sell it with the card. If the CD specifically says Airport on it, then I guess you can include it in the sale.
I guess you could take it out and sell it, if you're pretty sure you are never going to want it. What do you plan to do with the computer? Is it always going to be in an environment where you have only dialup, or is there a chance it will be in a high speed environment in the future?
You can remove it by yourself, but based on your knowledge level, you don't sound that comfortable with electronics to me. I don't mean that as an insult or anything, but if that is the case, please be very careful not to damage your iMac just to get $60 for the card!
Anyone who is basically familiar with the inside of a computer should be able to do it for you, though.