I forgot to mention the point that mph brought up. Try clearing your Cache and Cookies and try again. That may work? The experience that Laura described seems to indicate that the website is working to some extent.
Yup, I've done all that. Let me reiterate what I've tried.
At work:
My old laptop with Chrome and IE.
My brand new desktop, straight out of the box, Chrome and IE.
At home:
My old iMac with Chrome, FF, Safari.
My brand new iMac (old one died last week), right out of the box, Chrome, FF Safari,
My old MacBook, Chrome, FF, Safari.
Both places, with wifi and just over cellular network:
iPhone 6
All browsers have been reset and caches empty.
I've tried all of the websites offered in this thread.
I've tried different days, different trains, different times.
I've tried the trenitalia website on english and italian.
I've tried booking two separate tickets instead of one round trip.
I've tried booking an unrelated journey, adding it to my shopping cart, then booking the journey I want and still get the same error message.
It appears the error message has changed, and now reads: "Error code: 406 There is not enough seat availability for this request"
I'm genuinely out of ideas at this point.