OK now you've proven that my assumption that Linux Mint was causing the problem
Did you attempt to follow or understand
I suggest booting to Win and insuring internet connectivity - then while in Win discover the DNS that is being used, or the method to detect DNS
Reboot to Linux and insert the Win DNS server or choose a similar method to detect.
You now have another working option from which to choose settings - Fedora. You shouldn't have to go to the Library to discover the DNS entries for the 3 OSes that you've tried.
Obviously your hardware is just fine, and Win & Fedora must have different network settings than Mint. I propose that you proceed with the basic assumption that nothing's really broken but rather there's a setting incompatible in Mint that won't work at the Libraries!
isn't necessarily going to remedy your situation - trying different options (as you did with Fedora) can lead you to a solution
Post back with your results........