Here's my suggestion: use google analytics instead. Don't feel like a dummy. This plugin and its current installation design are not ready for prime-time. I can't make mine work either and I am a software engineer. LOL!
I think at some point when I upgraded I received akismet and opened a wordpress.com account. I don't remember doing that to get the API key, but I don't know the name of the account. It is a mystery to me. There was an API key already plugged into the field for it. I used it in the stats plugin config, and I received the same error message.
I tried making a new account. I used it for akismet, but I got the same error in stats.
I gave up and kept google analytics. At least this way I don't lose my archived stats and it is under the same account as my gmail, so I won't get confused or locked out.
This is a great idea - but the API key from an account on a remote site (wordpress.com) for self-hosted people is a PITA, and the instructions need a little work to get things unstuck if you are locked out of your stats for some bizarre reason.
Like all things wordpress - eventually this will get squared away with better design or better instructions to work with the current design, and it will be a good plugin.
I suggest you hold off for now.