If that's all you want for output, the following would do that. 
#!/usr/bin/perl
use strict;
use warnings;
use Inline::Files;

my %data;
while (<A>) {
    chomp;
    my (undef, $fragment, undef, $pos) = split /\t/;
    $data{$pos} = $fragment;
}

<B>; # throw away header '300     dG = -62.54 ...'
while (<B>) {
    my $pos = (split /\t/)[0];
    print "$data{$pos} $pos\n" if $data{$pos};
}

__A__
1-Match:    GGTGTTGTATGCCTTTAAA    5    3545
2-Match:    GGAAAGTCAAGCCCATCTA    9    3254
3-Match:    GTTCTTATTTGCACCTACT    6    180
4-Match:    GATGAGGAACAGCAACCTT    5    844
__B__
300     dG = -62.54   [initially -70.70] gi178893_M23263_rna_300-1 
1    G    0    2    0    1
2    A    1    3    0    2
3    A    2    4    0    3
4    U    3    5    0    4
5    U    4    6    0    5
6    C    5    7    0    6
7    C    6    8    0    7
8    G    7    9    34    8
9    G    8    10    33    9
........
........
179    A    178    180    231    179
180    G    179    181    230    180
181    U    180    182    229    181
........
........

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In reply to Re^5: Key value pair in hash inside while loop by Cristoforo
in thread Key value pair in hash inside while loop by newtoperlprog

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