Had the exact same issue with my friend. I bought the 4 pack on steam, gave him a copy. I could log into mine/his account on my PC. He could log into no account on his, but he could log into his/mine on his wife's machine. That narrowed the problem down to his machine being the issue.
I checked his log files (DemigodLog.txt), and he was getting:
info: 00:00:49: Error from CVP. Response XML:
The handle is invalid.
info: 00:00:49: >>>Entering CVPInterface::IsAppUpdateRequired()
info: 00:00:49: >>>Exiting CVPInterface::IsAppUpdateRequired()
info: 00:00:49: *DEBUG: OnHide: \000true
info: 00:00:49: MUSIC : Activating cue [Main_Menu]
info: 00:00:49: *DEBUG: OnHide: \000false
info: 00:00:53: >>>Entering CVPInterface::ClientLogin()
info: 00:00:53: >>>Exiting CVPInterface::ClientLogin()
info: 00:00:53: Error from CVP. Response XML:
The handle is invalid.
While I was getting:
info: 00:00:21: Error from CVP. Response XML:
<?xml version="1.0" encoding="utf-8"?><CVPGetApplicationInfoResponse><ResponseCode>0</ResponseCode><ResponseMessage>Success</ResponseMessage><WebServer>WALNUT1</WebServer><ApplicationData><ID>444</ID><ApplicationID>dem</ApplicationID><RegistryKey>Demigod</RegistryKey><NetworkRegistryKey>Drengin.net</NetworkRegistryKey><Ver d3p1:type="VersionInfoEX" xmlns:d3p1="http://www.w3.org/2001/XMLSchema-instance"><Major>1</Major><Minor>30</Minor><Revision>165</Revision><ServerType>1</ServerType><ProductionType>1</ProductionType></Ver><Versions><Ver><Major>1</Major><Minor>30</Minor><Revision>165</Revision><ServerType>1</ServerType><ProductionType>1</ProductionType></Ver><Ver><Major>1</Major><Minor>00[b]</Minor><Revision>074</Revision><ServerType>1</ServerType><ProductionType>0</ProductionType></Ver><Ver><Major>1</Major><Minor>30</Minor><Revision>165</Revision><ServerType>0</ServerType><ProductionType>1</ProductionType></Ver><Ver><Major>1</Major><Minor>20[b]</Minor><Revision>074</Revision><ServerType>0</ServerType><ProductionType>0</ProductionType></Ver></Versions></ApplicationData></CVPGetApplicationInfoResponse>
The solution we came up with (on windows 7) was disabling the firewall (domain, home, and public), disabling UAC, and checking the "run as administrator" option in the compatibility tab of the demigod.exe properties.
He can't run it with the steam overlay, he just double-clicks the demigod.exe now, but he's now able to log in. I also have windows 7, with my firewall and UAC disabled, but I can run it through steam and didn't have to do anything with changing how the program runs. Just a quirk I suppose.
Hope this helps!