All the information that you were given is correct. You purchased Lightroom as a standalone product, but somewhere along the line you have installed the creative cloud installation. It cannot be activated with the serial number because the creative cloud installation doesn't rely on the serial number. It is dependent upon your Adobe ID and password. The only solution to the problem you are facing is to uninstall Lightroom and then installed from this website:
Performing this uninstall/reinstall will have no impact whatsoever on the work you have done. Your catalog and associated Lightroom files will remain, as will all your images. Simply go through the process outlined. When you are finished you will still have a Lightroom icon on your desktop. All of you will have to do is double-click on that icon and go back to work. You'll find that your develop module will no longer be disabled.
Unfortunately this is a problem that is very common. It's very easy to locate and download the creative cloud version of Lightroom, but it's not so easy to locate the standalone updates.
You should never post your serial number on a public forum.
It seems to me that the Adobe CS rep could have given you the link to the Product Updates as Jim did but I think they’re not allowed to help on non-Cloud products or maybe just don’t want to be tied up in a chat for however long it takes for you to download and install LR.
It seems to me that if Adobe isn't going to allow CS reps to support non-cloud products then those products shouldn't be offered. But I suspect you're right.