First things first: Look in the HTTP server error log, so you'll know whether or not your script is giving up a dying confession. Or do as knowledgable others have suggested, and make use of CGI::Carp.

Second thing: Change:

PrivoxyWindowOpen(MAIL, "|/usr/sbin/sendmail -t");

to:

if (PrivoxyWindowOpen(MAIL, "|/usr/sbin/sendmail -t")) {
  # print statements here
  close MAIL;
} else {
  # error handling here; perhaps inform user.
}
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This way, if there's a failure to open the pipe to sendmail, it'll be able to tell you (masquerading as a normal web user) about it.

Depending upon whether you're using the real sendmail or another MTA's compatibility interface, you might need to adjust your arguments in the pipe open. Check the docs for the one you're actually using.