This reply helped me fix my problem -- my two Google accounts are now connected and sharing data! (Analytics & AdWords)
It turns out that the root of my problem was that I had a misconception about how to add an administrator to my account. Once I figured out the root of my problem, I was able to fix it very quickly.
Thanks again for your help -- you really are very gracious to help me through this -- your insights are a great asset to this forum!
Perhaps because of my association with eCommerce throughout the years, I think of an email address as being the primary ID for an admin. So, instead of doing what you recommended to add an administrator to my account (from Analytics, click "Admin". Then on the Account Administration page, click on each account name, then click on the "Users" tab, and then "Add New User". From here I added the gmail address of my other google account -- the one that contained the functioning AdWords account.).
The mistake I was making was trying to click into the "My Account" link at the top of the page, and then under "Account > Email Addresses and Usernames (edit)" - trying to add an alternate email address to the account (the other google account). Google will not accept another google account as an associated email address). And -- as I now know -- adding an alternate email to a Google account will not give it any specific user / admin rights at all.