Instead of:

if ($start_month == "04"||"06"||"09"||"11"){
[download]

You probably really want:

if ($start_month eq "04" || $start_month eq "06" || $start_month eq "0
+9" || $start_month eq "11"){
[download]

or even (using grep and "eq" for string comparison):

if (grep {$start_month eq $_ } qw(04 06 09 11)) {
[download]

or a hash.

But you probably really should use a CPAN module for this.