Thanks to Vladimir Svidersky, for fixing this issue for SQL Server 2012 SP1 with other servers running on Windows 2003.

After building the same environment as I have, Vladimir could repro the bug and tell us the hotfix for our Windows 2003 servers. It works like a charm. We had to fix WMI to provide additional properties Activity Monitor is expecting.

Hotfix

You will find the hotfix here: The number of physical hyperthreading-enabled processors or the number of physical multicore processors is incorrectly reported in Windows Server 2003.

The title is a little strange, but the problems should have the same reason.