You don’t have to use wireless for your Internet connection if you are within cable reach of your DSL or cable modem or router. Being “hardwired” into the network is faster than wireless, less prone to problems and more secure, too. (This won’t turn off the wireless for other users, though. To do that is more complex and you might not need to do that, anyway.)
What you need is an ethernet CAT-5 cable to run from one of the ports on the router or cable modem to your iMac. You can go directly from the cable modem to the iMac, or from your Time Machine or from other router. The length of the ethernet cable should be less than 20 feet or so and also be out of the way so people don’t trip on it. You may aleady have an ethernet cable left over from when the cable modem was installed.
First, turn off the Airport in your iMac by going to the Airport icon in the menu bar. (You can also remove the inactive icon from the menu bar in the Network Preference Pane. Click once on the Airport icon in the left hand pane and then untick “Show Airport status in menu bar.”)
With the Network Preference Pane open, plug in the ethernet cable and then click on Ethernet in the left hand pane. This will show your ethernet connection.
Most of the time, your iMac will automatically find the connection and connect. You’ll see a green dot that means ethernet is active, and see that you are “Connected” and the ethernet connection will move to the top of the list.
If your iMac doesn’t automatically connect, in the “Configure iP4” menu, select “Using DHCP.” That tells the iMac to automatically ask for a network address from the router. You may also need to turn the router off for a few seconds and turn it back on. If you get a warning that your iMac has a self-assigned IP address, restart your iMac.