Serial number would be in license.lic file present under DDM_Installation\cfg.
There are almost 1200 characters in that file. I pasted them into the "Serial # License Key" box of the product request and clicked on Next, but I got a message "There was an error" (no other details). I assumed the problem was the request needed a shorter serial number instead of the whole license key. That's why I originally posted this question.
The serial number could be Your DDM 'Product Order ID', I am not sure about that and not sure where you are giving this information.
If you want to get the new license file, I would recommend you to raise a Shipping Case (using Enter Online Support) or send an email to firstname.lastname@example.org. They would send you the updated license file.
Alternately, you can contact your Informatica Sales Representative, he/she should be able to help (getting new product license & renewal) you on this.
If this is for a partner key, just applying for a new download/license through the partner channel should also work. You'll get the current version as a bonus.