click on Manage account
click on (the first) Products
Click on "view your products" lists your software with license keys
Also you can find your product to download the product again but use your product key to
install it. So you see, you can always download the product. You actually buy the key.Otherwise you might want to explain how installing the product without a serial number is possible or how are you installing it, specifically each step. Maybe there's something new I don't know.
If you cannot install the product, then I cannot help you further, I'm sorry.