ssl on on ssl_cert_file server.crt server.crt ssl_key_file server.key server.key
Since I able to connect to both computers using psql and pgAdmin, I suspect the problem is with the connection within the Application. The connection string in the application is correct, and I verified the user name and password being passed properly.
Have you verified the other parameters, in particular the port. I am suspicious of the port='' in the above. The error is pretty straight forward, the correct host name is not being found in the the pg_hba.conf file. That means either the host name is not specified correctly in the file or you are connecting to a different cluster(port) then you think are and are picking up a different pg_hba.conf.