One basic problem is this: $Tids{$Tid}=$Tid; assigns a scalar to $Tids{$Tid} which is not what you want. The value of $Tids{$Tid} will wind up being a hash reference - not a scalar. I made some changes to your code below. Essentially take that line out! I can see from the error messages why you would have been driven to try \$Tid as a key, but that is not the right approach.

I would not use $Tid as a global. Pass it around when you need it. Check the value of the open of the file named "file" to make sure that it worked. Instead of using "a" and "b", why not use something more descriptive like the text that was in the file, ie FIRST_NUMBER, etc?

I could make some other comments, but the most important part here is to understand the multi-dimensional hash.

#!/usr/bin/perl -w 
use strict; 
use Data::Dumper;

# hashes
my %Tids=();

#open(IN,"<file") or die "unable to open file";

while(<DATA>) {

    if(/ORIGINATION_ATTEMPT/) {
        my $Tid = findTID();
        print "$Tid,$Tids{$Tid}{'FIRST_NUMBER'},",
                    "$Tids{$Tid}{'SECOND_NUMBER'}\n";
    }
}
#close(IN);

print "============================================\n";

foreach my $Tid (keys(%Tids)) {
    print "$Tid,$Tids{$Tid}{'FIRST_NUMBER'},",
                "$Tids{$Tid}{'SECOND_NUMBER'}\n";
}

print Dumper \%Tids;


## subroutines
sub findTID {

    my $line=(<DATA>);
    if($line =~ /Tid: ([0-9a-f]{8})/) {
        my $Tid = substr($1,3,5);
 
        $Tids{$Tid}{FIRST_NUMBER} ="----------";
        $Tids{$Tid}{SECOND_NUMBER}="----------";

        findNumbers ($Tid);
        return ($Tid);
    }
}

sub findNumbers {

    my $Tid = shift;
    my $line="";

    while($line=<DATA>, $line !~ /\-{30,}/) {
  
        if($line =~ /FIRST_NUMBER\s+(\d+)\s/) {
            $Tids{$Tid}{'FIRST_NUMBER'}=$1;
        }
        if($line =~ /SECOND_NUMBER\s+(\d+)\s/) {
            $Tids{$Tid}{'SECOND_NUMBER'}=$1;
        }
    }
}

=prints ###############################
d1234,9876,9999
a4321,1234,----------
a9999,----------,3333
============================================
a9999,----------,3333
a4321,1234,----------
d1234,9876,9999
$VAR1 = {
          'a9999' => {
                       'SECOND_NUMBER' => '3333',
                       'FIRST_NUMBER' => '----------'
                     },
          'a4321' => {
                       'SECOND_NUMBER' => '----------',
                       'FIRST_NUMBER' => '1234'
                     },
          'd1234' => {
                       'SECOND_NUMBER' => '9999',
                       'FIRST_NUMBER' => '9876'
                     }
        };
=cut ######################################

__DATA__
--------ORIGINATION_ATTEMPT--------
Tid: abcd1234
FIRST_NUMBER 9876
SECOND_NUMBER 9999
---------------------------------------
--------ORIGINATION_ATTEMPT--------
Tid: defa4321
FIRST_NUMBER 1234
---------------------------------------
--------ORIGINATION_ATTEMPT--------
Tid: defa9999
SECOND_NUMBER 3333
---------------------------------------
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