I was getting the same "User does not exist" error, but I found a workaround! I noticed that the email address stored in my account is written in all lowercase, but I was typing it with the first two letters capitalized. I know it doesn't really matter in the grand scheme of things, that's how I prefer it to be displayed, that's how I was typing it. I tried typing it in all lowercase, and it let me log in!
I have yet to try installing and playing a game though. I'll post again and report my results.
I'm using client version 1.5.40