Once you have a running postmaster, trying to connect to it with client applications can fail for a variety of reasons. The sample error messages shown here are for clients based on recent versions of libpq --- clients based on other interface libraries may produce other messages with more or less information.
connectDB() -- connect() failed: Connection refused
Is the postmaster running (with -i) at 'server.joe.com' and accepting connections on TCP/IP port '5432'?
This is the generic "I couldn't find a postmaster to talk to"
failure. It looks like the above when TCP/IP communication is
attempted, or like this when attempting Unix-socket communication
to a local postmaster:
connectDB() -- connect() failed: No such file or directory
Is the postmaster running at 'localhost' and accepting connections on Unix socket '5432'?
The last line is useful in verifying that the client is
trying to connect where it is supposed to. If there is in fact no
postmaster running there, the kernel error message will typically
be either "Connection refused" or "No such file or directory", as
illustrated. (It is particularly important to realize that
"Connection refused" in this context does not mean that the postmaster got your connection
request and rejected it --- that case will produce a different
message, as shown below.) Other error messages such as "Connection
timed out" may indicate more fundamental problems, like lack of
network connectivity.
No pg_hba.conf entry for host 123.123.123.123, user joeblow, database testdb
This is what you are most likely to get if you succeed in
contacting a postmaster, but it doesn't want to talk to you. As the
message suggests, the postmaster refused the connection request
because it found no authorizing entry in its pg_hba.conf
configuration file.
Password authentication failed for user 'joeblow'
Messages like this indicate that you contacted the
postmaster, and it's willing to talk to you, but not until you pass
the authorization method specified in the pg_hba.conf file. Check
the password you're providing, or check your Kerberos or IDENT
software if the complaint mentions one of those authentication
types.
FATAL 1: SetUserId: user 'joeblow' is not in 'pg_shadow'
This is another variant of authentication failure: no
Postgres create_user command has been executed for the given
username.
FATAL 1: Database testdb does not exist in pg_database
There's no database by that name under the control of this
postmaster. Note that if you don't specify a database name, it
defaults to your Postgres username, which may or may not be the
right thing.