You attempt to read from $data, yet never open it that file handle.
You changed the initial content of @data. (It should be empty.)
DATA shouldn't be used as an all-purpose file handle. It's a special file handle.

Fix:

#!/usr/bin/perl -w

use strict;

my $data_qn = 'data_file';

open($data_fh, '<', $data_qn)
   or die("Unable to open plot data \"$data_qn\": $!\n");

my @data;
while (<$data_fh>) {
   my @fields = split ' ';
   for my $row (0..$#fields) {
      push @{$data[$row]}, $fields[$row];
   }
}

use Data::Dumper;
print Dumper \@data;
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Update: Oops, forgot to re-add the my @data; that was removed. Fixed.

#!/usr/local/bin/perl -w
use strict;
my  @data;
my $file='data_file';

open( DATA , $file);
@data=<DATA>; ### already read all of $file into @data
close(DATA);
print @data;

while (<$data>) { ### can make this 'for ( @data ) {'
my @fields = split ' ';
for my $row (0..$#fields) {
       push @{$data[$row]}, $fields[$row];
    }
}
use Data::Dumper;
print Dumper \@data;
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@data=<DATA>;
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while ( <DATA> ) {
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While you're at it, you might want to look into lexical filehandles instead of barewords. Lexical filehandles really are the way to go.

Update: The for loop suggestion won't work because you'd be using the same array as what you're pushing into. I didn't notice they had the same name until I came back through the thread and saw ikegami's node. In order to use that, you'd have to change the name of one or the other.

The script works fine if I use "./<script_name> data_file". But when I hardcode the name of data_file, it doesn't work. I am sure it has something to do with "while (<>)" statement. Can anyone please advice how to proceed when we have datafile name hardcoded, and it is read in an array and then.......???

I personally believe that you should get familiar with some basic Perl: then you wouldn't be asking such an embarassingly trivial question. Anyway, here's your fish - you either want

• an explicit open as in:

  open my $fh, '<', $data_file or die "Can't open `$data_file': $!\n";
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  and then you would use while (<$fh>) instead of while (<>), or
• just populate @ARGV manually:

  @ARGV='data_file';
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