On 9/18/11 I found support.ea.com, which has a live chat with a queue that you can get into. Unlike the live chat (aka "Busy Signal") on the origin help site.
Support Links > Contact Us:
Filled out the form, used subheaders Account/Registration > Product Registration.
Then it gives you a choice between a phone call and live chat. I picked the live chat.
Took about 5 minutes to get through a 20+ person queue. The customer service person asked about my issue, I said "Can't download legally purchased games, tried on Origin and activate.ea.com several times." Was asked for the game names, the digital rights codes (find them in your confirmation email from when you bought the games), and the email used.
That particular session ended when I was upgraded to level 2 and never got a level 2 specialist (I waited 2 hours only to have it cancel on me, saying there were no specialists available and to try again later).
Tonight, I got another person and we resolved the issue. The problem? I'd bought the games under a different email account than the one I used for my Origin login. So I had to create a new Origin login using the email I'd bought the games under and there they were, waiting for me to download them.
There is currently no way to combine Origin accounts, but maybe they'll do that sometime later, eh?