you said MY router. what kind of router is that? how come you don't have full control of your router?
usually router will not block outgoing connection (some stupid software firewall does, but not hardware router), so you should not have problem accessing any port on the outside.
its my works router, i dont know make/model and i cannot access it for obvious reason. my computer doesnt have a software firewall so it is definatly the router that is blocking the port.
routers can block both incoming and outgoing connections so the assumption you made is incorrect.
this is a known problem when connecting through work/school that is why cp.frihost.org was setup as it uses port 80, general surfing port.
i assume it's a cheap home router because you say "my". notice the word "usually" there, not expensive enterprise level with built in firewall. if you said "my company's" then you will get different answer.
if it's blocking outgoing connection then it's not just router. it does have firewall. it's the firewall that block the connection. router just route. hence the name: router.
also, "router" which handle connection sharing is not really a router in a true sense. it is call a router just because it's kind of routing traffic between 2 different network (the Internet and your intranet) using NAT.
true route never block, it forward to most "cheap"/"weightless" available connection.