Testing doesn't require any special tools, just a VOM and safety precautions. You want to lift the car to get access to the starter; my preference is to put all four wheels off the ground, but you can get by by verifying several times that the car is in park;

You can test the solenoid by bypassing the ignition switch and jumpering the solenoid's power terminals with insulated cable. That should crank up the starter and spin the crank. If so, then the problem is upstream of the solenoid, like the ignition switch or the battery not putting out enough volt/amps. If not, then it's likely the solenoid.

BTW, the W201 190E is one of the last of the Mercedes passenger cars that a home mechanic can comfortably work on with basic metric hand tools. Enjoy.