On the PC that is activated, open OneCare and click on Help/About to verify the Subscription LiveID. If you are being prompted to purchase a new subscription on the other PC, it is likely that you are using a different LiveID.
If it is the same, please contact support -
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
(Note, use the PC where OneCare is working, so that it can validate your subscription and show you all support contact options.)
-steve