Well, you can work out if Q78 is NPN or PNP and the pinout. The footprint will give you an idea of the original package type and probable current rating. Pick something with a 50V rating and go from there?
Actually, I'm not sure about Q78. Looking through the other manuals, Kenwood used a lot of the 'S type' package, with the built -in resistors.
It seems they were particularly keen on the UN4212 and UN4112 22kΩ ones for NPN and PNP respectively.
Anyway, I believe that the pinout from left to right is Base, Collector, Emitter.
Assuming that;
The Base goes to I/O Port P4, pin 14 on the M50940-109SP CMOS microcomputer
The Collector connects to the opposite side of the relay coil to the 15v supply rail
The Emitter connects to VSS (0v) at pin 32 of the microcomputer
There is no signal at all coming from pin 14, and if I jump the relay coil, then nothing new happens on the W4040. All there ever is is a single LED showing.
Granted, the unit is currently disassembled, with just the main board and transformer, so I suppose it is 'possible' that the cassette players and relative pcb's need to be connected in order for it to turn on, however I'm not convinced.
This is where a manual would help.