Then the issue is with the institution's router or somewhere else over the Internet that is blocking your Mac.
Running a simple traceroute should be able to determine where that blockage could be.
For example, running the following command in the Terminal app, would trace the route between your Mac and the Apple servers: traceroute www.apple.com
A successful trace should show a number of router "hops" that would be made between them. If that trace hangs up somewhere in between is where the issue may reside.
You can certainly runs this test yourself, but I still think you need to work with your institution's IT staff to get this resolved. Good luck!