Thanks Art! This did it:

my $search_string = 'C04\w*'.substr($year, 2, 2).$mon.$day.'\w*.ORD_AP
+I';
my $dir = 'C:\\done\\';
my $file;
my $i;

opendir DIR, $dir;
my @file = grep {/^$search_string/} readdir DIR;
closedir DIR;

foreach $file(@file){
    print $dir.$file[$i]."\n";
    $i++;
}
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