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my %where = (
    status => ['Offered','Denied','Cancelled','Conditional Offer'],
    sent_email => { '!=' => [ -and => undef, '0000-00-00' ] },
);

use strict; use warnings; use feature 'say';
use Data::Dumper;
...
say Dumper \@bind;

__END__

SELECT sent_email FROM TblRequests WHERE ( ( ( sent_email IS NOT NULL 
+AND sent_email != ? ) AND ( status = ? OR status = ? OR status = ? OR
+ status = ? ) ) )
$VAR1 = [
...
  'Cancelled',
  'Conditional Offer'
];