It seems what you're actually asking about is behaving in different ways based on different servers, rather than checking a database exists: you want one configuration on one server, and a different one on another.

What you could do is check the contents of $ENV{'SERVER_NAME'} , and attempt to connect based on the contents of that. Maybe (it's a bit simple):

my $db;
if ($ENV{'SERVER_NAME'} eq '50free.net') {
  $db = DBI->connect (...); # your public server
} else {
  $db = DBI->connect (...); # your home server
}
if (! defined $db) {
  # there was an error
}
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