The first thing I would check is if the postgresql server is reachable using the psql command line tool. You may have already tried that but if not, that is always my first test.
David,
JFYI - you don't have to have the postgres server on the system for pgAdmin 4 to work.
pgAdmin 4 does not connect to the database server at the startup.
Yatma,
Please share the logs, as suggested by Aditya, to analyze the issue.