Networks

Have you tried giving rights to COMPUTERNAME$ in active directory, but not the user accounts - assuming it's a windows network and the computers are on a domain.

First of all, you don't have much information. We don't even know what kind of file server it is.

I'll assume it's a 2k3 file server for now.
When a user logs in and tries to access a share it checks user credentials, not computer credentials. So even if you explicitly deny access to a share based on computer name the user will still be able to access that share regardless (even from the denied computer). Putting computer names in permissions does have use. Anything that's done on a computer level will be affected by this share, but it sounds like what you want is user-based.

You can dig a little further into your OSI model and restrict traffic based on IP and/or port.

I don't know if this really answers your question, but hopefully it gives you more info to go on.

I may be missing something here as I have never had a need to do this particular configuration. Maybe someone else will be more helpful.