First, a single array element should be written like this:

$begindate_fields[2];
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and not like this:

@begindate_fields[2];
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The latter is an array slice. The warnings pragma would have told you this. You should always start your script with:

use strict;
use warnings;
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This will save you a lot of time and trouble in the long run.

Second, Date::Manip::ParseDate interprets your dates as MM/DD/YYYY, not DD/MM/YYYY. So 1988-12-13 becomes the twelfth day of the thirteenth month of 1988 — which does not exist. You need to swap the first and second array indices:

my $normalized_begindate = $begindate_fields[1] . "/" .    # Month
                           $begindate_fields[2] . "/" .    # Day
                           $begindate_fields[0];           # Year
my $normalized_enddate   = $enddate_fields  [1] . "/" .    # Month
                           $enddate_fields  [2] . "/" .    # Day
                           $enddate_fields  [0];           # Year
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Hope that helps,