I got the answer after a 2-hour chat session with the Adobe help desk.
LiveCycle Designer ES is being replaced by Adobe Experience Manager - Forms Designer ESor.... AEM Forms Designer ES.
Download AEM Forms Designer and your original license key from LiveCycle Designer ES will work to download AEM Forms Designer ES
Go to this link: http://www.adobe.com/devnet/livecycle.html
Then... toward the BOTTOM RIGHT of the page you will see a link that says, "AEM Forms Designer - 1139-1001-3886-4854-1284-1828"
Click on that link to download AEM Forms Designer. Then when it prompts you for your license key... use your original one from LiveCycle Designer ES. It will download (using WinZip). And VOILA! You'll be up and running in about 5 minutes !
Good Luck !