What network leaves 25 open and closes everything else? 25 is the one they close to prevent SPAM.

Can you browse? Your browser makes a outgoing connection via some random port to "port 80" on the server at the other end. Are they blocking you from connecting to any port other than 80? Why 53 is open?

Is this a "at work" situation? Leave a client running at home on 53 or 25 and then connect to it when you are work. It's going to be hard to keep it connected, but if you put the IP over and over in your host cache file it might work.

Tell us what network only allows 53 or 25? and why?