To answer your question, yes, EventSentry does ship with a built-in PostgreSQL-based database which listens on port 5432 by default. What database was already installed on that host?
The database is a component however and can be unchecked during the installation. You can check whether the database is installed by navigating to Administrative Tools -> Services; if "EventSentry Database" exists, then the built-in database is installed.
Since the collector does appear to attempt to connect, it seems likely that the database was installed, or at least was attempted to be installed by the setup routine. I would normally have you check firewall settings, but since the collector is usually installed on the same host as the database, this would probably not be helpfu.
Can you give us a little more information?
1. On which of the two hosts did you install EventSentry with the setup?
2. Is there full connectivity between those two hosts?
3. What database do you already have running?
4. Where are you seeing the above error message?