Also, you are aware that your form may be used to send spam, not only to your company but also to any other address, by (for example) setting the subject to "Hi!\nTo: somewhere@example.com"?
You haven't told us whether a file actually exists at the location that $Form{attachment} outputs. The -f test checks for that. As T: sounds like a (remote) network drive, it could also be that the webserver user (and thus, likely the Windmail user) don't have access to that network resource. A second test from within Perl could confirm that, as could obtaining the Windmail logs.
Of course, you can still simply copy MIME::Lite into your script, no matter how much reluctance you show.
I have now got to the bottom of the problem. The code was OK.
The issue was that the document that I wanted to attach to the email had to be on the same server as I was running the script on. I can live with that, but it would be more user friendly if it could be on any server! Any suggestions as to how that would be achieved?
I already told you. This is a user permissions issue. Likely the user your webserver (and thus your script) runs as has no access to network resources. This is usually a good thing.