It is clearer to use LABELS with redo and next... it only is used in the context of BLOCKS vs what you were trying to do inside a single statement. Get a copy of Randal Schwartz's Perl Book It will help loads.

  THAT: {
# Ask for input
print "What is the Part Number that you would like to look up?\n";

# Get it
my $PartNumber = <STDIN>;

# See if it's empty
print "There was no input" if ($PartNumber eq "\n");
  
 # Execute next Block
  THIS: {
    print "What is the Revision level for $PartNumber";
      my $Revision = <STDIN>;
  # Pattern match or test until finished
      redo THIS if($Revision =~/rev/g);
        last THAT if($Revision=~/bored/g);
  # or Repeat the part look-up again
    redo THAT;
      }
 }
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I left using next to your own discovery...