It took me a bit to finally find code that works for this, so here's hoping this will help you out. The code will connect to an SMTP server and send a message off.
Some SMTP servers require your full e-mail address, while others require only your username. Try both until it works.
sub sendmail
{
my $smtp = Net::SMTP->new('servername',
Hello => 'hellodomain');
$smtp->auth('username', 'password');
$smtp->mail("recipient_address");
$smtp->to('recipient_address"');
$smtp->data();
$smtp->datasend("To: ... \n");
$smtp->datasend("From: ... \n");
$smtp->datasend("Subject: ...\n");
$smtp->datasend("\n");
$smtp->datasend("...");
$smtp->dataend();
$smtp->quit;
}