When you activate on the new computer you need to use the same LiveID as you used on the first one. The key cannot be used again.
f 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 the reinstall or additional computer install.
-steve