Open OneCare and click Help/About to see your Subscription ID. That is your LiveID. If you need to reset the password, http://account.live.com
If you still have problems renewing, 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
Another option would be to abandon the current subscription when it expires. Uninstall OneCare and activate with a new LiveID and either purchase with a credit card or use a retail key/PIN.
-steve