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

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

open(DIR, $start_dir) ...

##</code><code>##

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

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