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.
On the first PC, open OneCare and click Help and then About to see your Subscription ID. That is the LiveID to sign in with.
If that is the LiveID you are using, but you cannot activate with that ID, please contact support.
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
For more information see Instant Help - http://help.live.com/help.aspx?project=onecarev2&mkt=en-us&querytype=topic&query=OneCare_PROC_FindLiveIDHelp.htm
-steve