iMac won't connect to internet either by wifi or ethernet

I’m assuming that other devices are able to connect to the wired and to thr Wi-Fi networks here and can get to the Internet.if you’ve not confirmed that, go test that. I’d also test from the iMac to another local device; to the Wi-Fi box or to the gateway/router/firewall box.

Boot into Safe Mode and run a wired and a Wi-Fimtest and confirm that the wired and the Wi-Fi networks you’re testing with are each set to use DHCP in System Preferences > Networks and try connecting again. What you’re reporting can be caused by add-on software; anti-malware, anti-virus, network minitoring and firewall tools, amd other such can and have caused all sorts of problems.

Have you tried restarting resetting the router?

Try setting up another admin user account to see if the same problem continues.

Isolating an issue by using another user account