Re: Command and Conquer Generals Zero Hour Multiplayer LAN
I'm assuming the Origin installer doesn't ask you for a serial? So they probably have a master serial key for all installations of Generals, hence the issue.
I suggest finding a keygen or some valid serial keys online, and changing the installed serial key via the registry.
https://www.youtube.com/watch?v=1ucmezZ1Zrs
Change both Generals and ZH keys so they're different for all players, then try and play. Let me know how that goes.