Download and activation of Lightroom 4 to a second computer

I purchased Lightroom 4 a couple of years ago ... not a "cloud" subscription, the separate program.

I want to install it on a new laptop.  I don't want to pay $10 + per month for a subscription to use a program that I have already purchased.

Adobe Customer Support has been of absolutely no help.  They could only refer me to www.Adobe.com/getsupport.  At that site all off the options relate only to the subscription products.  Complete run-around to try to use them.  Obviously, talking to a real person (even getting to a chat window) is a highly restricted privledge at Adobe.

How to I download a copy of Lightroom 4 which I already own?  I don't have the activation key or serial number any longer.