iMac won't recognize my home wifi, even with Ethernet

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Make a New Location, Using network locations in Mac OS X ...

System Settings>Network, top of window>Locations>Edit Locations, little plus icon, give it a name.

System Settings>Network, click on the little gear at the bottom next to the + & - icons, (unlock lock first if locked), choose Set Service Order.

The interface that connects to the Internet should be dragged to the top of the list.

Sys Prefs>Network>highlight the Interface you're using>Advanced>TCP/IP>Configure IPv4: Using DHCP.

If using Wifi, instead of joining your Network from the list, click the WiFi icon at the top, and click join other network. Fill in everything as needed.

System Settings>Network>choose interface>Advanced>Proxies Tab, make sure none are set, like for HTTP & HTTPS.

System Settings>Network, unlock the lock if need be, highlight the Interface you use to connect to Internet, click on the advanced button, click on the DNS tab, click on the little plus icon, then add these numbers...

8.8.8.8

8.8.4.4

1.1.1.1

9.9.9.9

Apply.