On the dialog "object types" I see:
Built-in security principals
But "Computers" is not there. How can I grant permissions for a computer user?
I'm doubtful that the server in question is joined to a domain for the reason that there are no "local" computer accounts, there are only "domain" computer accounts and that accounts for why the computer object type is not present. Can you verify that the server is in fact joined to a Windows domain? If so, what type of domain? Windows NT, 2000, 2003, or 2008?
Can you give us a screenshot verifying the domain membership of this particular server?
I see Built-in security principals, Service Accounts, Computers, Groups, Users.
Not that I have much clue what kind of object you are setting the security for, or on what OS.
I guess whatever item you are setting security on cannot have computer account security set on it?
What happens if you do it from the command line? e.g.