Why can't I connect to the App store with iPhone 4?

I have an iPhone 3 and just bought an iPhone 4. Both second-hand.

I put all my details in the 3, have been using it for over a year with no major problems. I can connect to the app store and usually download various free apps, games etc. No problems.

I tried doing exactly the same with the 4. Same password and login, same credit card details (never understood why you need these for free downloads) and even the same wi-fi, settings on the phone etc. I understand that date and time also are an issue. So those are the same too. And the timezone, and language and everything.

But no matter what I do, the iPhone4 (which is in a better condition that the iPhone 3 and also came “clean” with all defaults reset to factory settings) refuses to connect to the store. Which sort of makes it useless. Plus my SIM won’t even fit in there, so I can’t even use it as a phone (yet).