Have you told the router to forward the connections of the teamspeak server, to your machine?
Routers are connection sharing devices. IE, they handle all incoming and outgoing connections.
Outgoing connections are easy. They are just destined for the internet and only have one way to travel.
Incoming connections are a little harder, in that once they arrive in the router, it is left scratching its head. Which machine should it send it to? It can't pick a random one, otherwise it is pot luck on the connection working.
Instead, you tell the router to forward specific ports to specific machines.
See the routers manual for help on the needed config changes.