Hi Dennis,
Do you still have an active subscription with OneCare?
If you do. Activate OneCare with your original subscription (Live ID and password).
If you're not sure when your subscription will expire. In your old PC which have OneCare still running ang active. On the main screen of OneCare, click help on the right top of the screen, choose About. . . Subscription detail will be displayed. Live ID date and expiration of subscription.
Alternatively you can login to
https://billing.microsoft.com - use your Live ID to verify your subscription.
If any of my suggestions did not answer any of your questions. You may contact support.
How to reach support (FAQ) -
http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90