So have you determined the health of the fuse? If it is open then the only thing between the fuse and the batt contact is three SMT caps. I guess one could be leaky but it's highly unlikely. If you have 1K to ground on the bad radio (compared to a much much higher resistance on mine and your good one) it's not much, about 7 mA, but will drag a battery down given a few days.
To find out if there is a short or some some kind of excessive current draw you can try this. With your good portable, rig up a way to run it on a power supply (7.5 volt) or with the battery off the radio. You may have to get inventive with stripped wires and black tape and such, but see what you can do. Now hook up a meter in the positive power lead and measure the current draw as the radio powers up and goes idle. You would expect to see about the same on the bad radio. But before you try the bad radio, also connect in series on the power lead a small light bulb. A 47 bulb would be great but a small one like what's in a car glove box will do. Now hook up the bad radio and check current during power up using the bulb as a safety current limiting device.. If it is higher than the good radio or the bulb burns normally bright, STOP! The radio is pulling excessive current and components could be damaged. Troubleshooting this will require isolating circuits to see which branch is defective. Almost impossible in this radio save for a few things (like the PA by yanking the b+ feed). Even Kenwood depot, I would suspect, will throw up their hands and slap in a new TX/RX board and charge accordingly. Way too time consuming to be cost effective.
Now on the other side of the coin, you can measure little or no current while you try a power up. This is perfectly safe. You can now leave the power switch on, grab the schematic and the x-rays, and start working backwards with a voltmeter to try and figure out what is lacking (to the best of your abilities that is). I'll take mmckenna's route, check the fuse and switch. If it's beyond that, I don't have the time, the eyesight, nor the equipment to cost effectively try a component level repair. Depot it is.
But it does sound like you have sand, so here's my swag. If you confirm the fuse and switch are good, I would think the uP is not responding to the power on input, and the first place I'd look is the supply voltages that run it and the voltage regulators tied to that. I learned a long time ago as a FNG on the bench, if you stuck and don't know where to go, basic voltage checks usually lead to something.
Good luck to you.
P.S. Makes me think of a good antidote concerning shorts. Motorola Micors with a clamshell control head. They had a protection diode in the control head that would occasionally short, blow the ignition sense fuse and the radio would cease to power up. Now the righteous thing to do would be to split the head, replace the bad diode and the fuse, reassemble and close the call. I had a senior tech show me this (swear to god). The "easy" fix was to put a paper clip in the fuse holder, blow the shorted diode to kingdom come, install a new fuse in the holder and head out for an early lunch.
