I tried making a new account, the same thing happens: whenever I go to purchase a subscription and it asks me to log in again for confirmation, hitting the log in button just times out. For reference, on my old account, I had a subscription as recently as August 2018.
You shouldn't have to make a new account I'd think then.
Just curious, did you try it with the Sea Monkey browser? That digital river purchase site is really old code, maybe there's some silverlight in it somewhere.