I'm going through the same thing with an '85 500SEL ($300 delivered to my door in a "non-start" condition).

Check the forum posts for CIS problems.

The first thing to check is the fuel pump relay. Jumper the relay (it is located in the fuse box on the driver's side fender wall on my car). Pull the relay, (large black plastic box with a round "cap" on it), connect a jumper between the two rearmost side by side pair of contacts, and see if the pump engages. You will hear the pump "whir". Make SURE you have all the fuel lines TIGHT! Those vane style pumps spin the pressure up to 50 psi in no time flat.

If you hear the pump engage, disconnect the jumper, undo the fuel supply line to the distributor's front, left side (17mm wrench and a hold down bolt with a 10 mm head) and fit a rubber fuel hose over the end of the flair, I think a 3/8" hose will fit. Run the end of the hose into a 1 liter bottle sitting well away from the fuse box area, down on the ground or over on the other side of the engine, connect the jumper and check the flow. It should fill the liter bottle in about 30-40 seconds. Use a clear bottle and you will also have a view as to the condition of the fuel you are pumping. While you have the line disconnected, pull the fitting it goes into. You will find a strainer inside the fitting. Clean it out.

If you don't have the proper flow then change the filter. Do NOT bypass the filter or you will be making more problems than you already have! Go ahead and ask!

That's the FIRST steps to diagnosing the CIS systems. Do this first before attempting anything else.