The battery is charged
When I turn the key, accessories, glow-plugs, etc. come on...

Then when I turn the key to start the engine it goes *click* once, and nothing happens as if the battery is completely dead. The car started fine and ran three times earlier that day.

I'm afraid it's the starter. Does anyone have any other ideas or possibly a parts manual / diagram and instructions for removing the starter?

 

Not familiar with 190D, but try starting in neutral if it is an automatic. Or have you checked battery terminals, and chassis ground.

 

See this Thread: Diesel Discussions - Mercedes Forum - Mercedes Benz Enthusiast Forums

Another Test you can do is use your Volt Meter on the Batter and have someone else try to start the Car. When you hear the Click of the Starter see what Voltage drop you are getting.
If the Voltage Drops below 11-11.5 Volts your Batter is not holding the chage well or something in the Starting System is creating a higher than normal load and using up the Battery.

 

See this Thread: https://mercedesforum.com/forum/dies...problem-55068/

Another Test you can do is use your Volt Meter on the Battery and have someone else try to start the Car. When you hear the Click of the Starter see what Voltage drop you are getting.
If the Voltage Drops below 11-11.5 Volts your Battery is not holding the chage well or something in the Starting System is creating a higher than normal load and using up the Battery.