Maybe you cannot do it with redo but you can with while

#!/usr/bin/perl
use strict;
print "What is the Part Number that you would like to look up?\n";
my $PartNumber = <STDIN>;
chomp($PartNumber);
while (!$PartNumber){ ## while $PartNumber is empty keep asking
   print "PartNumber? ";
   $PartNumber = <STDIN>;
   chomp($PartNumber);
}
print "What is the Revision level for $PartNumber?\n";
my $Revision = <STDIN>;
chomp($Revision);
while (!$Revision){ ## while $Revision is empty keep asking
   print "Revision? ";
   $Revision = <STDIN>;
   chomp($Revision);
}
print "PartNumber: $PartNumber\n";
print "Revision: $Revision\n";
[download]

-phill