I think poolpi has answered the question as you stated it: show a count of how many times each distinct full-line string appears in a file. But your first attempt, trying to store a hash of arrays, made me think that maybe you want more information besides the number of occurrences.

The HoA thing would be useful if you wanted to keep track of the line numbers where each distinct full-line string appears. The number of occurrences per string is then just the number of elements in the array for that string:

#!/usr/bin/perl

use strict;

my %hash;
push( @{$hash{$_}}, $. ) while (<>);

print "Total\tLocations\tString\n";  # output a header line

printf( "%d\t%s\t%s", scalar(@{$hash{$_}}),
        join(",",@{$hash{$_}}), $_ )  for ( sort keys %hash );
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(updated to fix grammar in first paragraph)