I agree, it's probably in the ->Open(). This might help 3dbc debug it.

my $doc = $MSWord->Documents->Open('C:/temp/hyper.docm') or
    die $!;
[download]

As far as the document: my "hyper.docm" was just a very simple test document I created.

This is text
This is hyperlink.
This is text
this is another hyper.
[download]

... then on "hyperlink" and "another hyper", I used Word to create hyperlinks (to wherever), saved, and exited.

If you trust me¹ , you could run this script to replicate my .docm exactly.

edit: footnote 1: trust is earned. if I haven't earned it, don't run that code; I won't be offended. In general, it's a bad idea to download and run binaries that you have no reason to trust.