Good news, you can still track! Yahoo! Web Analytics will still track page views and identify a first-time or returning visitor from the cookie, as long as you have deployed the noscript part of the tracking code on all the pages you want to track.
Cookie (HTTP cookie) = A small text file sent to your browser by a web server. It’s used for authenticating, session tracking, and maintaining user-specific information about users, e.g., site preferences, shopping carts contents, etc.