Socket communication on WAN/Internet

I have a program that relies on Winsock for communication in between two computers. I have used the Winsock control for this. While the program now works fine on a LAN, I haven't tried it for clients connecting to the server on a WAN or by a dial up connection. While I've coded for the Internet connection, in case they wish to access the server through a dial-up connection, but I am not very sure of how it is supposed to work. Does the code for the Winsock control need to undergo any changes if the IP Address is not one on the LAN but on a WAN or just an Internet IP address? For those of you who have coded socket communication over the Internet with wininet.dll for the connection and the Winsock control for the communication, please advice me of anything else that needs to be done apart from the routine Winsock methods and a connection to the Internet using InternetAutodial and InternetOpen.