I'll give you some help, just enough to make it ocompile (without strict). Please take the appropriate measures to declare all variables until strict no longer complains.

Obvious errors:

• The end-of-here-doc marker must be identical to what's after the "<<". Your "__HTML__" should align to the far left of the script, and there shouldn't be a semi-colon after the "HTML" near the bottom. After all, a delimiter specified without quotes, can only be a bareword.
• The line with the multiple arguments for defined(). I think I'd make it

  if (defined($query_name) && defined($query_email) && defined($query_me
  +ssage)) {
  [download]

  to begin with, but I'm still not sure it'll do what you want. Testing for a minimal length of at least one non-whitespace character, for example using /\S/, seems like a proper sanity check to me. Oh, on that same line, you use the variable $query_message while further up, you're using $query_msg. See, that's one thing strict is good at, flagging which variables you used.
• Remove the commas after the "WRITEFILE" in the three print statements.

I think that's about it. I still haven't run it, but at least I got it to compile (without strict), using "perl -wc script.pl".