There won't be an activate button, that's a mistake in the Help Text/messages. The current version of OneCare has a link to subscribe. Clicking that link would be the same to create a new subscription or to add a PC to an existing subscription for both a reinstall and new install to another PC.
If you have an active subscription, which is what was created when you activated on the first computer, you need to use the same LiveID on the subsequent activations. If you are arriving at a screen to purchase or provide a token, you are likely not using the same LiveID as the subscription ID.
If you don't recall the LiveID you used for your subscription, you will need to contact support who can provide that information to you using your Key and/or contact information.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
Alternatively, sign in at http://billing.microsoft.com with email addresses that you have set up as LiveIDs and one will show your subscription listed - that would the LiveID to use to activate with.
If the activation dialog already contains a LiveID from a prior attempt or one used in trial mode, but this is not the one you need to activate with to associate it with your subscription, see this post for how to reset this - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2776450&SiteID=2
-steve
