To ask the stooopid question: Are you starting out by trying to download a free application?
To initially register with Apple and to set up the "None" option on the App Store, you must first download a free application. Then, you are prompted to go through the various steps of registration, one of which will be the option to use "None" as a payment plan.
If you first try to sign up by downloading an app that costs money, you won't see the "None" option.
So, try it with a free app and see if that works. If not, then I don't know what could be happening, because it should work. Maybe a quick call to the Geniuses at an Apple Store might help. Good luck.
Marilyn