Usually the ability to run PC applications depends on the local rights of the domain user in the PC itself. Your workstation environment uses roaming profiles and it sounds as if your PCs are heavily locked down and may use policies downloaded from the Active Directory on the Windows Server 2003. You may need to check the details of the SOE (Standard Operating Environment) and policies from the documentation or talk to the desktop specialist who created your standard desktop image and policies, if they are in use. Policies can limit the applications that a particular PC or user group can run.
As an experiment, you can also log into the PC as the administrator of the PC itself with the local administrator account or with a local login name which belongs to the local administrators user group (hopefully you know the local administrator password) on a PC which is a member of a domain, you can first create a local user with the same name as the domain user, enter the name of the server domain and select the user as a local administrator or Power User, instead of a Restricted User.
The above test may the the answer, but you need to check the policies imposed from the server.
