Why does a new Mac mini's internet connection work for one user but not another?

OP wrote " I set up a new user and low and behold the second user has got internet connection OK. "

Tell-tale sign.

Some Third Party Software that is loaded to your Original User Account that is not effecting the Second User Account

To skip the Q&A session, just download the Application Etrecheck directly from the Developer. 

It’s a diagnostic tool that doesn’t change your computer at all. It gives you a clear and easy-to-read list of both your hardware and software. 

You can get it for free or pay for extra features. And don’t worry, the report won’t reveal any personal information. 

Once you’re done, just copy and paste the full report using the Additional Text Icon.