Something like:

use strict;
use warnings;

my $file = <<FILE;
  ----------------------------
                       !   Optimized Parameters   !
                       ! (Angstroms and Degrees)  !
 ----------------------                            -------------------
+-----------------------------------------------------
 !      Name          Value   Derivative information (Atomic Units)   
+  !
 ---------------------------------------------------------------------
+---
 !       hc2         1.1136   -DE/DX =    0.0                         
+  !
 !       nc3         1.3392   -DE/DX =    0.0                         
+  !
 !      nch3       117.4979   -DE/DX =    0.0                         
+  !
 !       hn4         0.9929   -DE/DX =    0.0                         
+  !
----------------------------------------------------------------------
+--
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGr
+adGrad
FILE

open my $inFile, '<', \$file;

my $valueStart;
my $valueLength;
my $min = 1.0;
my $max = 2.0;

while (<$inFile>) {
    next unless m/Optimized Parameters/ .. m/GradGradGrad/;
    next unless $valueLength or /^(.*?Name)(\s*Value)/;

    if (! $valueLength) {
        $valueStart = length $1;
        $valueLength = length $2;
        next;
    }

    my $value = substr $_, $valueStart, $valueLength;

    next unless $value =~ /^\s*[+-]?\d+(\.\d*)?\s*$/;
    next if $value < $min or $value > $max;
    print $_;
}

close $inFile;
[download]

Prints:

 !       hc2         1.1136   -DE/DX =    0.0                         
+  !
 !       nc3         1.3392   -DE/DX =    0.0                         
+  !
[download]