OK, In QB go to "Manage Merchant Service", then click on the "Manage merchant account" tab. What do you see? Is the "Process with Web Store" ON?

If not, try to switch it on. Will take a day to work. If switching on does not work right, you will have to call them and ask them to do it for you. Don't get into any discussions with them about what 3rd pary web service you want to purchase or use. Just insist you want it turned on. Wait a day and it will work.