In this case it's time to get your own internet access. That is, you also need to talk to this network admin as my bet is they know how to fix this.
-> Be aware that I've heard this question before from some college students. The answer usually infuriates them.
Bob
Hi
I'm trying to connect a Playstation 4 to a network which only allows traffic on port 80. I have connect the ps4 to a laptop using a cable (bridge mode), and I'm using a vpn provider on the laptop which receives all incoming traffic through port 80. I'm able to obtain an ip adress on the ps4, as well as connecting to the internet. The problem occur when I try to connect to the Playstation Network (I manage to connect to PSN when I don't use the VPN, but then the NAT connection fails, hence the use of VPN).
This page tells me that PSN uses a wide range of ports to communicate: http://faq.en.playstation.com/app/answers/detail/a_id/168/~/what-are-the-firewall-%28tcp-and-udp%29-port-numbers-to-connect-online-with
My questions is it possible for the ps4 to communicate to my laptop through these ports (or at least some of them), and then use a program to redirect the data from the ports and forward them all through port 80 on my VPN connection?
Note1:
I have no access to the router whatsoever, so I can't open any other ports, port 80 is my only alternative.
Note2: I came over this site, but I'm not sure if this would solve it https://splash.riverbed.com/docs/DOC-1883
Cheers

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic