[Plugin: WordPress.com Stats] Not accepting my API Key

How is that an error? It’s supposed to link to your account.

There are a lot of people who gets same error (it’s an error, because after this message we end in never-ending loop). Maybe this one will help you: https://www.ads-software.com/support/topic/224510?replies=18

I’m guessing that WordPress.com Stats is a “dead” plugin now?

Does anyone know of any alternative plugins?

No, it’s not dead. It works fine, I use it currently, as do many thousands of other people.