Where do I go for help when purchasing an iOS developer program and the payment is refused?
This is a little confusing since you start with Apple's developer page to create a free developer account, which then places the appropriate item in the normal Apple online store. I'm also a bit confused, since you don't get to the activation step until you've paid for your program - so no money changes hands during the activation (or even renewal) on the developer site.

For billing and/or payment support, you should call the phone number for the Apple Store you are using (in the US, it's 1-800-MY-APPLE) to work out whatever payment issues you have. I wouldn'tbother calling Developer Support at this point, since you need to buy the item just as if you were buying an iPod or a Mac from the online store where you live. If you have a web order number, I still would call the main store and have them check the status of the order and refer you to developer only once they've made sure the payment is OK. They are best suited to assist you with the purchase / credit card / security code issues and the developer side only needs to see that you have paid and doesn't care if you paid with Credit Card, a loan, an Apple Store Gift Card or any other means of payment that Apple accepts.

Once you "buy" the program from the normal store, a second redemption code is emailed to you whereby you then have to log back in to developer.apple.com to complete the enrollment process by agreeing again to any documentation requirements they may have once they have reviewed the documents you submitted.

If you applied as a business, there will be a several day delay while you collect the documents you need and submit them. Normally they get sorted within a working day or two. Again, if you need to get a hold of the development team, the main Apple sales contact can know what phone number you should call based on which storefront you are using to purchase your paid developer program.