There are several things you can do to find the source of the problem. First, you can set Debug option when creating $smtp object:

$smtp = Net::SMTP->new('**.*.*.*', Debug => 1);
[download]

It will provide you with some debugging output about process.

Second, you may check values returned by the Net::SMTP methods. If method failed, it would return false.

And finally, I would recommend you to use some higher-level module for sending email: MIME::Lite, Email::Send