The reason of the problem is that when you run:

$H_count ++ and ...
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for the first time, the post increment operator sets $H_count to 1 and returns 0, i.e. a false value. Therefore, the statement following the and operator is not executed. The next time you run the same post-increment statement, it will return 1 (and subsequently other true values) and it will work fine as shown in the following test under the Perl debugger:

  DB<1> $h++ and print "foo";

  DB<2> $h++ and print "foo";
foo
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This would work fine with the pre-increment operator:

  DB<3> ++$i  and print "foo";
foo
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The solution suggested by swl is probably better because there is no hidden surprise in it.

As a side comment, please note that in these two code lines:

    $line =~ s/\r//g; # removes windows CR characters 
    $line =~ s/\s+$//; # removes trailing white spaces
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the first line isn't useful, because the second code line will remove all trailing white spaces, including the \r Windows CR character.