There isn't much point in registering Lightroom 4.4 because that version isn't supported by Adobe anymore. I don't know this for sure, but I'm guessing that the link provided to register that old of a version might not even be valid anymore.
You can enter the serial and use LR without registering.
Believe me I've searched for it!
Many suggestions on where to locate it but none deliver...
Please tell me where I can find it.
Isn't there some menu command under Help in LR 4 that allows you to register/enter serial number/(or whatever the word is)?
In a word, no
this is what happens when companies achieve something close to a monopoly
When you first start LR after a new installation it comes up with a dialog that wants your serial, and if it is an upgrade serial also a serial of an older version. This dialog comes up on every start until you enter the needed data.
You can skip the rest of the dialog where you enter your name and what not for registration.