I don't have a Diesel MB but I have operated 2 Diesel Chevy trucks for the past 20 years.
1) Your starter can begin to drag and prevent the engine from getting up enough speed to start. Take it to a starter or parts shop and they can test it for you. Diesel engines, as I am sure you know, run from compression ignition and not spark ignition. This explains the obvious lack of spark plugs. To get good compression and therefore cylinder heat you need good cranking speed and good glow plugs.
You can check your glow plugs for continunity with a meter but this may not show if they will actually work. Take the plugs out, connect them to a battery charger (8 to 10 amp capacity). Plugs should draw about 5 amps when good. Get a small cup of water and hang the plug in it about half way up the plug. Connect the plug and you should see the water boil slightly around the plug. What ever you do DO NOT touch the plug tip when it is connected. The tips of these plugs get very hot very fast. You will get a nasty burn long before you even realize that the plug is hot. You can touch the body and the tab where electrical connection goes but stay away from the business end.
2) Check your fuel system for water in your filters. I change both my filters on each truck each time I change the oil at 10,000 miles. It is cheap insurance. If you have enough water in your filters to cause your engine not to run you are in trouble. By this time the water has already blown the tips off your injectors. Take your injectors to a Diesel injection service and have them 'popped'. Most will do it for free. Remember that these people sell injectors, so if they tell you that your tips are bad you might want to try a couple of other places and ask to see the spray pattern. Don't go to Mercedes for this. Chances are good that they send their injector work out to the same places that you can use.
3) If, before you go to all the above trouble, you are going to try using an ether type Diesel spray start, DISCONNECT your glow plugs. You can bend a connecting rod if you don't.
4) If you can push start your car it means that your fuel solinoid is opening and that your fuel is good enough to run your car. You can drain some fuel into a clear glass and see if the fuel is clear or cloudy looking. If it appears cloudy you might need to drain your tank, remove it from the car and thoroughly clean it.
5) My trucks start w/o having to push the gas pedal down. You should only have to let the plugs cycle once before the car starts. One of my trucks starts in less than one revolution. It will start on a hot day w/o using the plugs. But remember that each car is different and each has its own little tricks, but a well running Diesel should fire off almost instantly.
6) Low compression will make a Diesel hard to start but if you can push start it it has enough comporession to run.
For beginers, I would get the starter checked out and make sure that it is turning at the right RPMs.