Two problems:

• Single quotes don't interpolate variables. Make that "|mail $mail" for starters..
• Secondly, you're using || instead of or. || binds much tighter than or, causing your line to be parsed as follows:

  open MAIL, ("|mail $mail" || die "mail problem: $!");
  [download]

  ..which is probably not what you want. Make it:

  open MAIL, "|mail $mail" or die "Mail problem: $!";
  [download]

  to make it do the Right Thing.

perl -pe '"I lo*`+$^X$\"$]!$/"=~m%(.*)%s;$_=$1;y^+*`^ ve^#$&V"+@( NO CARRIER'