CIFS mount works when I specify IP address, but notwhen I only specify hostname

Oops, I think I figured out my last problem -- permissions were set wrong
on the mount.cifs executable.  Now, however, I get an error that says :

mount error: could not find target server.  TCP name mycomputer/c not
found  rc = -1073743160
 CIFS VFS: Error connecting to IPv4 socket. Aborting operation
 CIFS VFS: cifs_mount failed w/return code = -111
mount error 111 = connection refused

Not exactly the same error, but now what?