App Store Problem 'Payment Declined' (big problem)

I have an iPad 3, which is updated to 6.1.3 (I have heard there is 6.1.4 but it will not update me, tells me it's all up to date when I try)

Saturday night, I went to update my apps and a notification came up saying 'Tap Continue and sign in to view billing information'. So I signed in and then another box popped up with payment details.

In red at the top, I get this message:

'There is a billing problem with a previous purchase. Please update your payment method'.

This is odd for two reasons:

1) I haven't actually purchased anything in a long time, and I know for a fact that the app store and itunes do not allow you to buy things unless funds are present in your account. The only thing I've downloaded are free samples of a couple iBooks.

2) I am putting in the correct payment details in an attempt to fix the problem, yet it is still declining it (it just says 'your payment method was declined', but it isn't giving any more information.

I cannot update any apps or even download free apps. My iPad is effectively frozen to anything new and I don't understand why. As I say: nothing has been purchased on this iPad or on my computer in a long while, and those things I have bought before are of course already paid for.

This is very concerning. What is going on? I can't find anything specifically related to my problem anywhere.

I would appreciate responses from people who know the answer: conjecture sadly won't help much here!