Another way, which will also list all modules which modules you use, use:

$ perl -MDBI -e 'print qq{$_ => $INC{$_}\n} for keys %INC';
Carp.pm => /usr/lib/perl5/5.00503/Carp.pm
DBI.pm => /usr/lib/perl5/site_perl/5.005/i386-linux/DBI.pm
AutoLoader.pm => /usr/lib/perl5/5.00503/AutoLoader.pm
strict.pm => /usr/lib/perl5/5.00503/strict.pm
Exporter.pm => /usr/lib/perl5/5.00503/Exporter.pm
DynaLoader.pm => /usr/lib/perl5/5.00503/i386-linux/DynaLoader.pm
vars.pm => /usr/lib/perl5/5.00503/vars.pm
[download]

So, you could do:

sub() if exists $INC{'DBI.pm'};

Now, for how to know if the connection is open, I would also suggest Apache::DBI, so you can have a persistent connection.

Cheers,
KM