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. You can't use the same key twice - hence the 8059 error message. 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://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
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://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
-steve
Microsoft MVP Windows Live / Windows Live OneCare Forum Moderator
