Ok, I have another idea;)

I got in my job many Dell and lenovo laptop who present some problems with ethernet chips.
The problem is as follow: under certain conditions the network card is blinking, but there is just no link to the active component behing the network link (router/switch)...So as you seems to experience right now.

I found a workaround: go into BIOS, desactivate the network card, reboot. Then go to BIOS again reactivate the network card. For dell computers, I also have to uninstall the network driver by hand, and at second reboot time, the driver just reinstalls itself alone.

I tourns out that each time, this was a working workaround. For Lenovo computers, I found that if there is not enough electricity, the network card is just broking (end shutting down the computer doesn't resolve the issue obviously). So I have replaced all netgear switches we can find in meeting rooms by proper cisco switches, and there is just no more problems.

So now, the problem is: How would you desactivate the network card on a macmini, then reactivate, although I have one, I do not plug my hands on it too often to know the right way to do it (if any).