no, DBI is not the only way. there is also a Perl interface to PostgreSQL that comes as part of the PostgreSQL distribution called Pg. if it was not installed by your administrator, you'll have a harder time installing it than DBI/DBD::Pg. try running perl -MPg to see if you have the Pg module installed.

as for not being able to install DBI because you are not root, you should see How do I keep my own module/library directory?.

no version of Perl has DBI built-in (except perhaps a specific port).