How can I play NFS MW through the Internet using the "LAN Play" mode ? I try yo play with a friend but we're not in the same network. We have Internet connections and we played FiFA 06 and Counter-Strike through direct IP. NFS MW doesn't support this. We tried to make a fake LAN using Hamachi but the game still won't work although the "fake" LAN seems to work.

Don`t worry! There is no sugar.

Nope, I don't think there's a way to support this. The internet isn't a LAN, it's a WAN (wide-area network).
Now there was one program I read about that let you trick some of the Gamecube's LAN games into going online, but I don't know if it's still around or if they continued to work on other programs, perhaps for pc.

Download Battle.LAN 0.5
It worked with that.