Hello Gogreenby,
Thanks for reaching out to the Apple Support Communities! I understand you were experiencing an issue with "DNS Resolution Failure" being reported by diagnostics.
You did a great job thinking to run the diagnostics. If the issue is still occurring I believe that you'll find this information helpful:
The DNS is the Domain Name System. This is what allows you to type in a website address and reach a website. It translates the website address into the numeric address where the website lives on the internet. Typically the DNS is provided by the ISP that you're using. First, check the DNS settings. Here's how: Specify a DNS server on Mac.
Highlight any DNS server which may have been manually entered, and then click on the [—] to remove it. Once all are removed, the router for the network you’re connecting to will assign the DNS server. You should then be able to get online.
If you haven’t manually entered any public DNS servers, try restarting your MacBook Air into safe mode with these steps: Use safe mode to isolate issues with your Mac. Once at the desktop, please try connecting to the network, and see if the captive portal page appears. If it does and you’re able to login, try restarting your MacBook Air and see if you can connect again under the normal startup.
All the best!