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The common approach universities take is instead of restricting specific ports while allowing all, they will restrict everything and allow specific ports.
The ports you listed are both nonstandard, so you're probably being restricted under the "global restriction" policy. It takes a lot more effort to determine what program's data is flying through a port- I'm 99% positive that they don't know bittorent from anything else that would use the port.
NAT error is probably because you are part of the university's subnetwork. Other bittorent clients cannot determine your pc's IP. Probably because you don't have your own IP address. Instead you probalby have one for the local network and the school's mainframe exists as your gateway.
The NAT error could also be a result of you changing ports. It's not enough to change a port on the bittorent client and receive data- you have to get other clients to send you data on that port. This can't be done without changing the tracker to specify a different host port.
Unfortunatly, I believe you're out of luck. If you do manage to get bittorent working on some random port, the university would notice the abnormal change in network activity and block the port as a percaution. Universities are very much against Torrenting as it eats up bandwith needed for the rest of the campus.
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