This thing has been sitting around for ages and one way or another it has to go.
It's probably reasonable to give this thread a week and if nothing evolves then I'll scrap it for the components.
If I'm honest, it doesn't seem to me that the missing transistor is the reason that the unit doesn't turn on, however without the schematic, I'm not really sure where to start looking. The power supply section has one +12v and one +15v 78xx series regulators which are both fine. I haven't really tested the multitude of electrolytics nor semiconductors. There is one relay which appears to be activated from tape deck A and not likely to turn on the whole unit.
Working back from the power button, one side leads to I/O Port, pin 14 on the 64 pin main microprocessor IC, a Kenwood branded M50946-109SP, although which pin it passes through after that is another question? The other side of the power button goes back to pin 56 which is a high-voltage I/O Port.
As it's Sunday, I'll have another look and follow up here if anything else comes to light.