Your current directory is not always the same as the directory in which your script resides. Try specifiying the absolute path instead of just start, or try

use File::Spec::Functions qw( catdir rel2abs );
use File::Basename        qw( basename );

my $start_dir = catdir(basename(rel2abs($0)), 'start');

open(DIR, $start_dir) ...
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Also, readdir doesn't return a full path.

use File::Spec::Functions qw( catfile );

foreach (@files) {
    my $file = catfile($start_dir, $_);
    ...
}
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