PostgreSQL won't start: "server.key" has group or world access

Whenerver I start PostgreSQL using command:

$ sudo /etc/init.d/postgresql start

Pg doesn't start up. The error reported is:

 * Starting PostgreSQL 8.4 database server
 * The PostgreSQL server failed to start. Please check the log output:
2010-01-21 22:10:00 PST FATAL: private key file "server.key" has group or world access
2010-01-21 22:10:00 PST DETAIL: File must be owned by the database user or root, must have no write permission for "group", and must have no permissions for "other".

... and when I try to access psql as the postgres user with:

$ sudo su postgres
$ psql

it gives me an error:

 could not connect to server: No such file or directory
    Is the server running locally and accepting
    connections on Unix domain socket "/var/run/postgresql/.s.PGSQL.5432"?