This snippet makes a few assumptions and glosses over a few implementation details:

• Assume the input is well formed; "yes" or "no" always comes at the end of a complete module and ID definition sequence.
• Ignoring details about the file's "doc" encoding (which I assume you have already figured out).
• Ignoring details about your $Sheet object (again assuming you know what to do once data has been properly extracted).

Given those assumptions the following snippet will parse the file and place each "module/id" pair into an anonymous array, with all of them pushed onto an array poorly named @results.

use strict;
use warnings;
use autodie;

my $filename = 'something.doc';

my @results;

open my $in_fh, '<', $filename;

my( $module, $id );
while( my $line = <$in_fh> ) {
    chomp $line;
    if( $line =~ /^Module:\s+(\d+)/ ) {
        $module = $1;
        next;
    }
    if( $line =~ /^ID:(\d+)/ ) {
        $id = $1;
        next;
    }
    if( $line =~ /yes/ ) {
        push @results, [ $id, $module ];
    }
}
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It may feel unclean allowing $module and $id to retain values from one iteration to the next, even after a 'no' in the 'Customer:' field. But as long as the input is well formed, $module and $id will always contain valid information at the moment a 'yes' is encountered.