One possibility: you need to export the environment variable so that programs you run in the shell will see it. Like this:

export POSTGRES_HOME='/usr/wherever'
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When you say you installed postgres, how did you do that? Did you install the postgresql-server-dev or libpq-dev package that it said it required, or something else? You have to install the 'dev' package because that gives you the include files for compiling programs (including DBD::Pg) against the Postgres libraries. The include files (like postgres.h) are what it's searching for and failing to find.