Launching Word surely requires access to a 'desktop' (and 'windowstation'). If you aren't logged in, there may well be no desktop. (Even when you are not logged in, a Scheduled Task might not be run in a security context that gives it access to your desktop.)

http://support.microsoft.com/kb/165194 talks about how to use CreateProcessAsUser() to have a virtual (hidden) desktop and windowstation created so a GUI application can be automated.

I'd probably use Win32::API to be able to call CreateProcessAsUser() (which I'd use to re-launch Perl to run the script that does the real work).