The Booster is a dumb power amplifier. There should be some kind of signal wire or cable connection between the main PA and the booster. That's what it sound like is missing. (Like a telephone type wire and connectors, usually 4 wires.) Your looking for the command station connector I think, since I have NCE and that is what they call it.
To check your other connections, remove the PS4 input from the Booster and jumper over the PS input from the PA. In other words, feed both sides of the PS4 from the PA and see if it works. If it does, you need the signal cable from the PA to the Booster.
If you already have this signal connection between the two, it may be a bad cable or wired wrong.
Elmer.
The above is my opinion, from an active and experienced Model Railroader in N scale and HO since 1961.
(Modeling Freelance, Eastern US, HO scale, in 1962, with NCE DCC for locomotive control and a stand alone LocoNet for block detection and signals.) http://waynes-trains.com/ at home, and N scale at the Club.
Is the PA connected to the booster?
Paul A. Cutler III************Weather Or No Go New Haven************