There is no distinction between a subscription of OneCare and versions. All 1.6 users will be upgraded to 2.0 as long as the subscription is active.
If you installed OneCare 2.0 prior to mid November, you are running the beta and need to uninstall and reinstall from http://onecare.live.com
If you have a new install from the production site, and you are trying to activate with your confirmed LiveID, make sure that you are not pasting the password, but are typing it in. There is a bug in 2.0 that prevents the copy and paste of the password from working.
What version of 2.0 do you have (Help/About) and when did you install it and from where?
-steve