$file contains just the file name, not the path to the file. Fix:

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

opendir(my $dh, $dirname)
   or die "can't opendir $dirname: $!\n";

while (defined(my $filename = readdir($dh))) {
    my $fq_filename = catfile($dirname, $filename);
    my $mtime = (stat($fq_filename))[9];
    print "$filename: $mtime<br>";
}

closedir($dh);
[download]

I also made the following changes:

• I made the variable names more consistant ($filename is similar to $dirname).
• I converted the variables into lexicals. (How come you're not using use strict;?!)
• I converted the handles into lexicals.
• I removed the line number from the error message. You shouldn't need the line number in error messages about IO failures. You have a poor message if you do.

I didn't fix the bug where you print out plain text when HTML text is expected.