The code is as following:

36  my $prefixSysDescr      =   quotemeta 'system.sysDescr.0 : DISPLAY
+ STRING- (ascii):  ';
......
53      for ( $sysDescr ) {
54         /\Q$prefixSysDescr\E/ && do {
55            $sysDescr =~ s/$prefixSysDescr//;
56      print $sysDescr, "\n";
57      Pause(__LINE__);
58            s/^$prefixSysDescr//g;
59            last;
60         };
61         /^$prefixSnmpWalk/  && do {
62      Pause(__LINE__);
63            $sysDescr =~ s/^$prefixSysDescr//g;
64            last;
65         };
66      #   $sysDescr = $sysDescr . " " . $sysDescr;
67      }
68      print $sysDescr;
69      Pause(__LINE__);
...
[download]

The script runs straight to line 68. If I omit \Q and \E it matches

You're double encoding, you use one or the other, not both.

#!/usr/bin/perl --

use strict;
use warnings;

my $base = 'system.sysDescr.0 : DISPLAY STRING- (ascii):  ';
my $one = quotemeta $base;
my $two = "\Q$base\E";
print "$_\n" for $base, $one, $two, "\Q$one\E", "\Q$two\E";
__END__
system.sysDescr.0 : DISPLAY STRING- (ascii):
system\.sysDescr\.0\ \:\ DISPLAY\ STRING\-\ \(ascii\)\:\ \
system\.sysDescr\.0\ \:\ DISPLAY\ STRING\-\ \(ascii\)\:\ \
system\\\.sysDescr\\\.0\\\ \\\:\\\ DISPLAY\\\ STRING\\\-\\\ \\\(ascii\
+\\)\\\:\\\ \\\
system\\\.sysDescr\\\.0\\\ \\\:\\\ DISPLAY\\\ STRING\\\-\\\ \\\(ascii\
+\\)\\\:\\\ \\\
[download]