It looks like you need to store up your $NUM17 values in an array, and you also need to store up your RES-val pairs in a hash. Then, after you've read and stored the whole mess, go through the array and print the corresponding hash values. Like:

my @requests = ();
my %lookups = ();
while (<FILE>) {
    if (/^# input/) {
      push @requests, (split)[1];
    }
    elsif (/^\s\s\d+/) {
       my ($RES, $val) =  (split)[2,4]
       $lookups{$RES} = $val;
    }
}
print join("\n", @lookups{@requests}), "\n";
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It's not clear to me what the $NUM17 and $NUM18 business is all about, or what $etc is for. What I've done is assume that $etc indicates which $RES to look for, to print the associated $val.