No idea what the problem is but please specify which train(s) exactly you are trying to book (origin, destination, date, departure time), since there are often alternative ways to book.

I was booking trains from London to Paris, Paris to Barcelona, Barcelona to Montpellier and then Montpellier back to London. 

I finally got it to work by doing it reservation by reservation.  My best guess is that there was some computer glitch.

That's a known issue on the reservations website, and you found the workaround.

How did you get this to work? Having the same issue. I’m unable to make a payment. I am redirected every time I am asked to put in my billing address 

Book each train separately.

But the advice from the experienced travellers in the community is to use other ways to make reservations than the Interrail/Eurail website. You can look at the guide in the link:
https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105
If you, after having looked at the guide, have questions about how to make specific reservations, please create a new topic with your travel details (departure date, time and route) and you will get advice.