OK... I just realised you may need to forward a port on your router for the net game to work properly. I haven't tried it (the net part) myself yet but I'll let you know if you need to open a port and we'll cross that bridge when/if we get to it. Either way, you will definately need to set your firewall to allow PES6.exe to connect to the internet so let's just start there.
I haven't worked with Norton for a while but I think you need to go into Norton Internet Security and do the following (roughly, some words may not be exact but that shouldn't make much of a difference):
Click "Firewall" or "Personal Firewall" ...or whatever the tab says. Clcik "Configure" on the tab that opens up.
Clcik the "Programs" tab. Go over the list of programs and see if PES6.exe is there and, if so, if the Firewall is set to "Block all". If it is, change that to "Allow all".
If you don't see PES6.exe on the list, click "Add" and browse to it in your c
program files\konami\pro evolution soccer 6 folder (or wherever you installed it). Make sure it is set to "Allow all" before you exit.
And that should be it for the Norton Firewall. If you are also running the Windows Firewall, disable it (control panel->windows firewall) as running both is redundant and troublesome.
Once you have done this, try running the game and connecting again. Let me know how it goes and good luck. Don't worry, you can't really do anything harmful to your firewall if you just follow the instructions above.