I assume that the new laptop is runnign Windows 7.
Installation of Windows Live OneCare in Windows 7 is not supported. You can use the free Microsoft Security essentials for malware protection - http://www.microsoft.com/security_essentials/resources.aspx
See this post for End of Life information for Windows Live OneCare - http://social.microsoft.com/Forums/en-US/onecaregeneral/thread/81996436-edad-41ba-bdfc-02fc094e2ca9
If the laptop is running XP or Vista, and your subscription still has time left on it, reinstall or add a computer from http://onecare.live.com - member accounts - add a computer. Activate with your LiveID for your subscription.
Personally, I'd install Microsoft Security Essentials - be sure to remove any trial or installed security software from the PC first.
-steve
~ Microsoft MVP Windows Live ~ Windows Live OneCare| Live Mesh|MS Security Essentials Forums Moderator ~
