Looks like it is working now. I am not sure if the service is backup. But I also did the following:
Went to: https://shopping.turbotax.intuit.com/unified/downloads?cgcview=downloads
Logged in to my account
Added, my product key here by clicking "Enter your license code here". It gave me a popup to add product code. I entered the product code from my Amazon order
After that I launched the Turbox and it fetched the license from my account.
May be it is looking for product code to exist on your account
