Your LiveID should be visible as the Subscription ID when you open OneCare and click Help/About...
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 - and then click the renew link next to the subscription.
Alternatively, uninstall OneCare when it expires (it will autorenew if you used a credit card to subscribe, so no need to do this in that case) and install and activate with a different LiveID and a retail key or credit card.
-steve