Your router is probably using NAT. So, your Internet provider gives you a real, globally routable IP address. Your router than gives you a private IP address:
192.168.x.x
172.x.x.x (there are 172. addrs that are real, but I doubt your provider has one)
10.x.x.x
Your router than does some magic and translates your private IP address into the routers real address. This lets you share that one IP addr that your provider gives you with a bunch of other computers.
Your solution will involve port mapping. You will need to see which port your file sharing is using. Go into the:
Control Panel -> Sharing -> Firewall, and look at the numbers that are next to the services. What you want to do is look at your firewall configuration (probably a web page) look for something like "port mapping" and then tell it to map the port numbers next to the service in the firewall control panel to the IP address that your computer is using. Look in the network control panel to find out what it is.
Manually setting your IP address will only mess things up, and will NOT fix your problem. Your router is giving you a reasonable address, if you are going to use a router.
I am assuming that you have a reason to use a router in the first place. If you only have one computer, you don't need it, unless you are using wireless and airport, since apple stupidly does not allow you to make pppoe connections over airport, and most ISPs require pppoe for broadband.
Hope this helps