I'd be surprised if it is the key switch. That doesn't seem to be a very common failure mode. They sometimes stick but ususally the switch is still good. I took a look at the EPC and it looks like the solenoid can be ordered separate although I don't see it in PartsShop. On the other hand the start assembly is only $216 at PartsShop versus $700 on the EPC.
One way to determine if it is the switch or the starter is to jump 12V dirctly to the solenoid with the key off. If it starts then but not with the key then it must be the key switch or the wiring.
I don't know for sure where the starter is on this car. I've never messed with mine. But gernally speaking they are usually on the passenger side of the motor down low. Access it from underneath.
1984 300D Euro