I did talk to support via chat, and although the 2 people were polite, the solution did not come from there. This is the solution:
Go to this page https://www.adobe.com/account/account-orders.html
Look for My order history
Find the product by date, order number and on the right there is a download button.
Download that product file. If you don't want to use the Akamai manager, you can just get the file under "other options". The key was that the number did not work with the trial version.
The trial version is the one that is available on the web site. When you search, you find that. The key is that you need to download the exact version you purchased. This could perhaps have bee, stated somewhere near the lines about how you will need a serial number, because the way the downloads page is worded, it looks like you can download the trial and install it and use your serial number.
Look at this page: Download CS5.5 products - below is what is shows.
Thank you for taking the time to help. Adobe could add one sentence to the above page that would have saved me at least two hours:
"If you have already purchased this product, go to the downloads section of your page and use the download files there, not these trial versions."