I am a member of physics stack exchange and am able to access my account in it. But after chat was enabled on my account I could not log in as it said my account didn't exist. At the same time I am already logged in in the physics site of stack exchange
You seem to have the requisite reputation (and had it at the time this question was posted, too), so it should just work. Can you try again. Possibly the chat system didn't notice right away that you had enough rep.
If that fails I'm out of my depth and we'll look for someone who knows more.