You mention that the computer is attached to a router? What type of router is this? Do you know if the router provides any type of firewall type protection? If so it might be blocking your attempts to connect through it.
If you have access to another machine that you can place on the same network, you should try to see if you can succeed in being able to ssh to the box without the need to go through the external interface on the router. If you do not have access to another machine, you can come close to simulating this by simply trying ssh to the box from itself (try ssh'ing to both its IP address and 127.0.0.1).
Assuming that you can ssh to the box locally, but still cannot do so remotely I would think that you need to take a real close look at the router. You will have to ensure that it is forwarding your request on port 22 to the box that you are running your ssh daemon.