That help process is terrible, in my opinion. The 20 digit code is the product identifier that you will find in Help/About in OneCare, which you can't access since you can't install.
To reinstall OneCare, first run the cleanup tool:
Cleanup tool - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=828910&SiteID=2
Then install from http://onecare.live.com and activate/subscribe with the same LiveID you originally subscribed with.
If you need help, and OneCare is not installed on any PC in activated form for your subscription LiveID, you'll need to follow the steps to get email support as a trial user.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
-steve