Bad koolgirl. I gave you nice clean code and you nastised it. Here are a few guidelines to help make it nice again:

1. define variables where they are first required
2. use the three argument version of open
3. use lexical file handles (ones declared with my)
4. avoid nesting if
5. don't slurp files and such (for loops implicitly slurp)
6. show the name for failed opens along with the OS's error message
7. don't comment block ends. If you avoid nesting, keep blocks short and indent nicely there is no need and it removes clutter

and the niceised code:

use strict;
use warnings;

my $dir = 'F:\project_files';
my $fInName = 'carson_county_abstract.txt';
my $fOutName = 'cars_abstract.txt';
my %docs;

opendir my $dirScan, $dir or die "Failed to open $dir: $!\n";

while (defined(my $entry = readdir $dirScan)) {
    next if $entry !~ /docs(.*)/;

    my $currParcel = $1;
    my $filePath = "$dir\\$entry";

    open my $inFile, '<', $filePath or die "Can't open $filePath: $!\n
+";
    while (defined (my $line = <$inFile>)) {
        chomp $line;
        $docs{$line} = $currParcel;
    }
    close $inFile;
}

open my $fIn, '<', $fInName or die "Failed to open $fInName: $!";
open my $fOut, '<', $fOutName or die "Failed to create $fOutName: $!";
while (defined (my $line = <$fIn>)) {
    next if $line !~ /Document #: ([0-9]*)(.*)/;
    print $docs{$1} . "\n";
    print $fOut "parcel# $docs{$1} doc num $1 $2\n";
}
close $fOut or die "Error closing $fOut: $!\n";
[download]

To fix your duplication problem you might want to use another hash to check for duplicate document/parcel pairs.

Ok, and if you don't understand stuff find a friendly web site dedicated to the area and ask for clarification ;).