Actually, you should be using the JetPack plugin now, not the stats plugin. Automattic (the team behind WordPress.com) have begun bundling their stats system with a few other features (social network sharing, LaTeX support, to name a couple) and aren’t updating the older systems any more.
JetPack will use oAuth to connect to your WordPress.com account and will automatically select the right blog. If it doesn’t, you should contact their support team directly to ask for help.