How about you strip your code down to a small sample script that is sufficient to show the error. Something like:

#!/usr/bin/perl
use strict;
use warnings;

my %hash;

while (my $line = <DATA>) {
    chomp $line;
    next if $line =~ /dG\s=\s(.*?)\s/;

    my ($sNum, $nt, undef, $connect) = split(/\s+/, $line);
    $hash{$nt} = $connect;
}

foreach my $key (keys %hash) {
    print "$key\t$hash{$key}\n";
}

__DATA__
300     dG = -62.54   [initially -70.70] gi178893_M23263_rna_300-1 
4    U    3    5    0    4
5    U    4    6    0    5
14    G    13    15    30    14
15    A    14    16    29    15
16    G    15    17    28    16
18    A    17    19    26    18
19    C    18    20    25    19
[download]

which prints:

A    19
C    20
G    17
U    6
[download]

Note that you don't need both -w and use warnings. Best to omit the -w as shown in the code above.