I've never used Win32::OLE before or this object, but I'm guessing it's:

my $reports = $DOM_document->DocumentElement();

foreach my $report (in $reports->childNodes()) {
   foreach my $report_child (in $report->childNodes()) {
      if ($report_child->{'nodeName'} eq 'report-name') {
         print($report_child->text(), "\n");
         next;
      }
   }
}
[download]

Update: I initially forgot to put in the calls to childNodes. Fixed. Tested. Works.

By the way, the following is a better error message for loading:
my $DOM_document = Win32::OLE->new('MSXML2.DOMDocument')
or die("Unable to load object MSXML2.DOMDocument: $^E\n");
It's more descriptive, and the $^E will display why it wasn't able to load the object.