Does sound like the server document has had access rights changed in the security tab to not allow your users access.
The recommndeation as above. (Backup names.nsf)
Shutdown server, copy names.nsf to worksattion and open locally, go to servers view and locate relevant server document.
Select security tag and check the fields (
Access server: Not access server:
)
If unsure of correct setting then use blank in both fields and it will allow all certified users access.
Save document, close client and copy the names.nsf back to the server and start it up again. and see if it shows the same errors.