Well it might depend where the domain name came from. Did you get given a tiscali customer domain name, the one you use to get on the site. E.g.
www.tiscali.co.uk/~yourname
Or did you get given webspace, and you purchased another domain that linked to it. e.g.
www.yourname.co.uk.
If it was the former, you need to ring tiscali and ask them to let you download the files that you left on their webspace. You would then need to either use webspace from your current ISP, or some other company. The tiscali webspace that you were using is there because they haven't bothered to delete it, but you wont be able to change/access it since you no longer have a tiscali account.
If you bought your own domain name, and simply pointed it to the tiscali webspace, then you need to go to the place you purchased the domain from, and redirect it to some new webspace. Does this make any sense?
Whatever the situation is, if you're using a tiscali domain name, you wont be able to rebuild the site using the same name. They wont give you access until you're a customer of theirs.