If I understand what you are trying to achieve then you can do it using a single regular expression match:

use strict;
use warnings FATAL => 'all';

my $count1 = 0;

my $line = do {local $/; <DATA>;};

$line =~ s/\n//g;

while (($line =~ m/(?:aaggt){2}([atgcn]{100,})/ig)) {
    $count1++;
    print " $1\tcount1 \t $count1\n";
}

__DATA__
aatgatgataaggtaaggtatgatgatgatgatgatagtagannnnnnnnnatgcatgaatgcaatgact
+agcaatgac
tagcaaggtaaggtaaggtaaggtaaggtatgatgatgannnnatgatgactagactgacaaggtaaggt
+aaggtatga
tgatgatcgatgacgat
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As an aside, note that you should always use strictures (use strict; use warnings;). You should also use the three parameter version of open and use lexical file handles:

open my $inFile, '<', $fileName or die "cannot open $fileName: $!\n";
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