Cannot Connect To Localhost Using Windows Security Group As Login

I have a test environment set up at home with a small windows server 2003 Active Directory domain. I created a windows security group on the dc and added myself and another user to the group. I then use this group as a login for SQL Server and add the login to the sysadmin server role. This works exactly as I would expect on the Windows Server computer (which is also the Domain Controller) regardless of which computer I use to connect to this Windows Server computer. However, when I set up the exact same login on the local sql server instance of my client laptop running windows xp pro, the I get an error message (Login failed for user MYDOMAINdgolds...) when I attempt to connect to the local instance of SQL server, even though I am able to connect to the instance on the domain controller with no problems using this same client laptop under the same user account. The only way I am able to connect locally on the laptop under this account (which does not have local admin privileges on any box, for testing purposes) is to add the user account separately as a login, rather than as part of a group. I'm curious as to why being a member of a security group that is part of the sysadmin server role does not allow me to connect to the local instance of SQL Server on this client laptop. The windows server computer is running SQL2k5 Enterprise, and the client laptop is running SQL2k5 developer. Any insight into this would be appreciated.

Thanks,

Dave