I'm in a similar situation (in that I still have a LineOne PAYG account, which has a LineOne email address and a couple of Tiscali email addressess hanging off it.
I think that if you try dialling the 0845 661 4681 no. from your telephone handset you'll get a message saying that this number does not accept calls from withheld nos. (even if your phone isn't withholding your no.). So this is why you cannot connect and creating a new connection won't help. BTW, I think a more recent number is 0844 057 5000, but I get the same result with this as well.
Like you, I tend to have connected periodically (every 90 days in my case) on the LineOne account in the hopes of ensuring that it is kept active. Although I have to say that I've never seen anything that says that Tiscali (and more latterly TalkTalk) require such action. Freeserve (part of Orange these days), did explicitly state that one had to dial-in every 90 days to keep an account active (and I still do this for such an account as I still have a website active of the free hosting that they supplied back then).
Interestingly, I also have a Onetel dial-up account (also part of Talk Talk these days), which DOES still work. Again I dial-up every 90 days.
I've not had any problems receiving emails sent to my LineOne address (even though I know that the password does not conform to their current security specs. This might be because I don't actually login to the LineOne address as I have any emails arriving there automatically forwarded to one of the Tiscali email addresses (where the password does conform due to some changes I made just 2 or 3 weeks ago). The other Tiscali email address password does not conform either (but also forwards automatically to the Tiscali email address that does conform). BUT, I can use Outlook Express to check for email on these non-conforming accounts without any prob (of course there's never any email in these due to the auto-forwarding).
Of course, like you, I am concerned that these email addresses are going to suddenly stop operating. I've kept these addresses active to avoid having to notify all and sundry each time I change ISP. Plus I have separate addresses for specific purposes (e.g. general correspondence, online purchases, business, gumf registering on websites etc.)
Maybe it's time to switch across to using something like gmail.