Reading the documentation for Email::Folder::Exchange, it looks like this module works through the Outlook Web Access.
If you do not have Outlook Web Access enabled and want to access an Exchange Server without Outlook, you will have to use CDO (Collaboration Data Objects) which provide a COM based API to connect to a MAPI store.
I connected to Exchange through Perl using Outlook Redemption which allowed for better script integration.
As for getting the current user and password information, I am not sure how this would not be a major security hole!
I have not tried the Win32::IntAuth but maybe this would allow you to impersonate your Exchange user and connect via CDO/RDO as mentioned above.