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 the activation dialog on the laptop 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
You can review your subscription status by signing in at the Billing site: http://billing.microsoft.com
If the subscription on the Billing site shows your account as active and that's the same LiveID that is refusing to be accepted by the activation process on the laptop, I recommend that you contact support.
-steve
