(2-part post):
I don't use a Mac so I apologize if this post is a bit vague but I hope that it will point you in the right direction:
SMTP servers, provided by ISPs, are normally set up to only allow connection from customers of that ISP. This is why you can't send via the Tiscali SMTP server. However, it's often possible to receive mail through a POP3 server, even if you don't have an account with the relevant ISP. (Some ISPs enable you to receive e-mails through their server for an indefinite period after you terminate your subscription. Others only allow you to do so for a few months).
So, if you want to be able to continue to receive e-mails sent to your old e-mail address, it's important that you don't delete your old account details from your Mac. You need to add a new account, without deleting the existing one.
Here's where things get a bit vague: Exactly how you set up a new account, on a Mac, isn't something I know about. With most e-mail clients, (irrespective of the operating system they work under), you usually need to look under 'Tools' and then 'Accounts'. If you can't find something similar with your e-mail client, I suggest looking in the help files for the program.
Once you've found the way to create a new mail account, you simply need to fill in the relevant information. See here:
http://www.adsl4less.com/broadband-support.htm