Hi @AnotherElk, I’m now sure that ‘USB debugging’ was not activated. Unfortunately, I cannot get to that option since the unlock code was forgotten. I have tried another cable, which allows me to get to ‘fastboot’ with my Fairphone. To get it to connect to my Fairphone, i had to first to go to ‘Developer Settings’ and select ‘usb debugging’ and accepted the popup that allowed me to pair my phone with my laptop.
This guide about using ‘fastboot’ explicitly says that I need to have USB Debugging enabled.
I am hoping that you are right and I don’t need to have USB debugging enabled when connecting the phone to a new laptop, but I think I am missing something. : ( 