I had/have a similar problem with my
fishing boat. It has a
Volvo TAMD41B in it, but I think the wiring in the instrument panel is very similar.
Do you have the 16 wire harness? A key start switch? High temp, low
oil pressure
alarm? If so the wiring is probably almost the same.
My problem was that the engine would start itself, but only on nights with dense
fog. I burned up two starters and two seawater impellers, luckily the
noise woke me up (light sleeper) both times so the engine wasn't fried.
After much
head scratching, manual reading and perusing of wiring diagrams, I figured out that I couldn't figure it out; there was no way for the engine to start itself unless there was a fault allowing
current to get to the start relay which would then activate the starter
motor. So I cut my losses and just installed a battery switch that isolates all
power to the starter when in the off position. Just have to remember to turn it off!
But I didn't leave it at that. Hate not being able to figure things out. I still was of the opinion that the problem was in the ignition switch, because of the high humidity tendency to autostart. So I pulled the panel and was removing the ignition switch when I noticed that there was some kind of fault or short in the 16 pin harness connector; I could hold it one way and everything was fine, another and the panel died. So, (since I'd already been kicking around the idea of making my own harness thereby eliminating Volvos' exorbitantly priced and (in my opinion) overengineered
electrical system), I figured I'd find the problem by process of elimination. Cut the red main positive supply, bypassing the connector, still shorts,
Cut the purple gauge positive supply bypassed the connector, still shorts. Wait a minute, no difference with 2 hots what about the ground? Cut it, bypassed the connector, everything works fine. (actually better, there used to be a anomaly; when the gauge panel lights were on the temp read high and the
oil pressure read low, now they stay the same with the gauge panel lights on or off.)
Well that problem
solved, back to the ignition switch. Took it out, turns out that the
Volvo switch is (typically) complicated. The
electrical part of the switch is separate from the key cylinder, and a dirt dauber had made a nest in the space between the actuating lock cylinder and the actual switch. So I cleaned out the nest and ohm checked the different positions. Checked out ok, so I squirted WD40 into the lock cylinder and as well as I could into the electrical part of the switch. Ohmed it again and still checked ok so I put it all back together.
Had the boat out yesterday for about 6 hours and everything worked fine, no autostarting, but since I'm not sure that the actual cause was the dirt dauber nest (or maybe
salt built up inside the switch), I still turn the main switch off when I'm not on the boat.
At some point I will probably make my own harness, eliminating Volvo from the electrical side of the engine completely. I already have a Delco
alternator, aftermarket
gear reduction starter, and Teleflex gauges, I retained the Volvo ignition switch because it operated the start, run, kill and glow plugs all in one, but at a 250.00 replacement cost a fully sealed 4 position ignition switch for 25.00 and a momentary pushbutton for the glow plugs makes a lot more sense practically and economically.
Realize this is long winded, but hoping it illustrates one way of looking at a similar problem. If you have a push to start switch, with an on/off key and a mechanical kill (As I've installed on the MD2020 in my sailboat) then your problem is somewhat simplified. The start switch typically operates a relay which operates the solenoid which operates the starter. First, with an ohmmeter check that the start switch operates correctly. If so, then check the wires in the start circuit, which should all be yellow and red (though of different gauges at different points), a visual and electrical check from the start switch to the relay to the starter solenoid should be made, and any problems corrected, (corrosion, loose connections pinched wires). You can check the relay with an ohmmeter and a battery, but it may be easier to swap the one from your properly operating engine.
My guess would be starter switch, start relay or harness/connector short.