It has taken me several days but I finally got my ticket!
The museum website is only able to process ticket payments thru the green PayPal link at this time.
Thanks for the info! I hope to be able to buy my October tickets soon.
If you have a European credit card that works too. Since the service only began in July, I am sure they will start taking American credit cards soon.
The nice man who answered the phone at the main number for the Pantheon told me their online ordering system was not fully working correctly and so the only link on their online system available was the green PayPal link. That’s how I ordered my ticket.