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 are using the correct LiveID, but your password is not being accepted, change the password to be shorter than 8 characters at https://account.live.com and then try to activate.
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 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://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/f5ce50e4-9165-40a5-891b-fe5d0659738b
For more information see Instant Help - http://help.live.com/help.aspx?project=onecarev2&mkt=en-us&querytype=topic&query=OneCare_PROC_FindLiveIDHelp.htm
If all of the above do not help and you are still unable to activate on the 2nd PC, please contact support.
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare, Live Mesh, & MS Security Essentials Forums Moderator