Who is your ISP? Comcast? Time Warner?
When you say "the server IP was added to the router" do you mean you created a DHCP reservation for the 192 IP your server is using? Or do you mean your setting your server to use your static IP?
If you have a Static IP from your ISP, then that should be set Under your "Internet Settings" also known as your WAN IP. Also, if going from a DHCP IP to a Static IP, most ISP will require you to call them, and on request, will clear your ARP cache.
As for the internet working until you start a torrent, sounds like your downloader is using up all your bandwidth.