iMac losing Internet, but not wifi

Thanks for posting in the Apple Support Communities brianburgess,

Safe mode can be used as an effective way to isolate whether software that loads automatically at startup, might be causing an issue or conflict.

Complete the following steps, and test to see whether there's any change:

1: Turn on or restart your Mac, then immediately press and hold the Shift key as your Mac starts up.

2: Release the key when you see the login window, then log in to your Mac. 

3: You might be asked to log in again. On either the first or second login window, you should see ”Safe Boot” in the upper-right corner of the window.

If the issue continues in safe mode

If the issue continues while in safe mode, or your Mac restarts several times and then shuts down while starting up in safe mode, you should reinstall macOS and make sure that your Apple software and third-party apps are up to date.

If the issue doesn't continue in safe mode

If the issue doesn't continue while in safe mode, leave safe mode by restarting your Mac normally. Then test for the issue again. The issue might be resolved.

If the issue returns after leaving safe mode, startup items are probably at fault. Apps can install such items in numerous places, and they aren't always easy to find or recognize. For that reason, you should first make sure that you've installed any available updates for your Apple software and third-party apps.

If updating your software doesn't help, try any of these solutions:

• Test your login items.

• To learn whether software in your user account is causing the issue, set up a new user account, then log in to it and try to reproduce the issue in that account.

• Unplug all accessories from your Mac, including printers, drives, USB hubs, and other nonessential devices. You could have an issue with one or more of those devices or their cables.

• Reinstall macOS.

• If you still need help, please contact Apple Support.

How to use safe mode on your Mac

Cheers!