When you activated OneCare on the new PC, did you use a new LiveID and a new retail product key or did you activate with the LiveID for your original subscription? If you already had a subscription, technically, you should not have been able to use the same key to activate on the new computer and would need to use the LiveID for your original subscription. Sign in at http://billing.microsoft.com with your LiveID to see the status of your subscription. If OneCare on the PC does not match what you see on the Billing site, I believe that your PC date and time are likely incorrect.
-steve