To install and activate on the second PC use the *same* LiveID used to subscribe on the first PC.
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 - 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.
-steve