If you check description for the InternetDial on the MSDN
http://msdn.microsoft.com/library/default.asp?url=/library/en-us/wininet/wininet/internetdial.asp

you can see that on success this function always returns ERROR_SUCCESS, which is 0.

On the other hand, 631 is an error code -- ERROR_USER_DISCONNECTION.

Check [Internet Options - Connections] -- if they are identical on all computers. It could be a difference for that unlucky one.