Corporate networks will usually be defaulted to rules like this:
deny all; allow 80; allow 443; allow 21; allow 22; etc...
It is much easier to configure this way rather than to explicitly deny 99% of the 65,535 available ports.
With that said, I took over a client-facing portal which used a non-standard port due to network limitations; I do not know the NAT details. Anyways, this made it impossible for about 50% of our users/visitors to access site and whenever they would call us to report this issue, we would have to coordinate with their non-existent IT to try and get an allow rule implemented.
I do not know the details of your infrastructure limitations but I would imagine that something else is running on 80/443
If this is the case then your only shot might be to use an internal proxy or upgrade the switch to something with more advanced NAT capabilities which can route the requests appropriately.
Don't use a non-standard port for public-facing services which already have a standard port.