Ethernet connection iMac OS Majave

At a bare minimum you should do a NVRAM reset per the directions in https://support.apple.com/en-us/HT204063 and also restart in Safe Mode, this restart can take up to 10 minutes to do. Instructions for the Safe Mode restart are in https://support.apple.com/en-us/HT201262.

After doing both, then retest, if you still have problems try another Ethernet cable.

Finally, I am assuming you have set your Network Preference to have Ethernet as the top priority in System Preferences - Network.

Okay, what troubleshooting have you attempted on the iMac? Chances are there is nothing wrong with the hardware. It may only need a NVRAM reset or to restart in Safe Mode or it may even be a bad Ethernet cable.

Read my reply. You have to reset the cable modem to get it to work with another piece of equipment. And reset it *again* to re-use your friends computer.

If this is something you want to do all the time, you friend will have to get a router and call the cable company to reset the modem so it will accept the router. Then you can change computers at will.

What are you connected *to*?

If it is a cable modem, the evil cable company often restricts plugging new equipment into the modem. You might have to call them to reset it.

It is not a modem "problem," just that the modem will only recognize one computer until you reset it.