I'm sorry to read about the theft and hope that you are successful in getting the PC returned to you and the thief apprehended.
Assuming that OneCare is still running on the stolen PC, and it connects to the Internet, the local law enforcement agency with an active case can contact Microsoft and request this information officially. Law enforcement has a special number to call (I do not know this number) and they will need to take care of the legal paperwork to make the request. They will need to know your subscription information, PC name, and other information related to the account and that PC.
On your new PC, simply activate OneCare (subscribe) by signing in with your subscription LiveID to associate that install with your active subscription.
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://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
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://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2776450&SiteID=2
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
