Computers in a group cannot access a single file from server

We use Server 2008 RD. We have a group in the Active Directory with several computers in it. The group has access to a single file but none of the computers in the group can actually access it. I created another group using the computer's users and they were able to access the file. All were members of the domain. Did I miss something? We need to work by computer and not by user. I would appreciate any help.
