Hi Jmaccormack,
We understand your computer is connected to a Wi-Fi network, but the internet is not working. We're happy to offer some guidance.
If you haven't already, we'd recommend restarting the computer to see if that helps.
Log out, sleep, wake, restart, or shut down your Mac
If you have any type of security/anti-virus/VPN software installed on the computer, you can try disabling that to see if the internet works with it turned off.
You can also try starting the computer in safe mode to help rule out ant 3rd party software as the cause of the connection issue.
Start up your Mac in safe mode
You may also want to try forgetting the Wi-Fi network then reconnecting to it. To remove the network just go to System Preferences > Network > Wi-Fi, then click the Advanced button, select the Wi-Fi network you're connected to then press the minus button at the bottom to forget the network. After that just reconnect to the network and test out the internet.
Connect to the internet with your Mac
If the internet still will not work when connected to Wi-Fi, we'd recommend contacting Apple for assistance: Get Support
We hope this helps. Take care!