my $db;

eval {
   local $SIG{ALRM} = sub { die "connect timeout\n" };
   alarm 15;
   $db = DBI->connect("DBI:Oracle:".... ) or die $DBI::errstr;
   alarm 0;
};

if ($@) {
   # timed out
   die unless $@ eq "connect timeout\n";
}
elsif (!$db) {
   # didn't connect
   die "no database connection\n";
}

# $db is ok here