Also, you dont need the second loop - You can make use of the fact that you are using a hash.

use strict   ;
use warnings ;

my @data = <DATA> ;
my %freq_hash ; # What you call '%hash' 

foreach my $single_line ( @data ) { 
    chomp( $single_line ) ;
    my ( $word, $freq ) = split( / /, $single_line ) ;
    $freq_hash{ $word } = $freq ;
}

## So far all we have done is get data ## 

print "\nData Before Process:\n";

foreach my $word (sort { $freq_hash{ $b } <=> $freq_hash{ $a } } keys 
+%freq_hash ) {
    print "$word\t\t$freq_hash{$word}\n";
}

foreach my $word ( keys %freq_hash ) { 
    if( ( lc( $word ) ne $word ) and $freq_hash{ lc( $word ) } ) {
    $freq_hash{ lc( $word ) } += $freq_hash{ $word } ;
    delete( $freq_hash{ $word } ) ;
    }
}

print "\nData After Process:\n";

foreach my $word (sort { $freq_hash{ $b } <=> $freq_hash{ $a } } keys 
+%freq_hash ) {
    print "$word\t\t$freq_hash{$word}\n";
}


__DATA__
the 1
The 1
hello 15
hell 19
Hell 8
[download]

Update: Included code.