I have a 88 260E that had a similar problem. Your car should have two fuel pumps in front of the rear axle on the passenger side. Remove the plastic cover to access the fuel pump/filter assembly. Attach a voltmeter to both of one of the fuel pumps power terminals and check for voltage. When the ignition switch hits the RUN position you should see a short pulse of 12 VDC to pressurize the fuel system. When the ignition is in the START position you should see 12 VDC constant or until you stop cranking.
If you never see power at the pump i'd suspect the fuel pump relay which is located behind the battery. There are two large black relays and one small one just behind the ABS computer. Just lift the ABS computer out of the holder and lay it aside. No need to disconnect the wiring harness just lay it out of the way being careful not to short the battery leads. The fuel pump relay will be the one closest to the battery and will look identical to the one behind it but they are not the same as the pinouts are very different. The smaller one mounted to the right is the overload protection relay.
From here you have several options. First check that the relay is fully inserted into the base. A loose connection here can cause multipule problems as the fuel pump relay is a multi contact device controlling more than just the fuel pumps. Push down firmly to insure the relay hasn't simply worked loose. Give it a good thump after you've seated it properly. Mine would go intermittent and only required a good thump to get it going again.
Second remove the relay and use a jumper wire to manually power the pumps. Check the wiring harness for your particular model and obtain the correct pins to jump. The holes that the relay plugs into are numbered to make identification easier. Unless you know exactly what pins to jump don't attempt this as you may cause a short and fry your ECU or worse. Use a short lead of wire to power the pumps just long enough to verify operation. You should not attempt to run or drive the car in this state this is for diagnosis only. Your only attempting to get 12 VDC at the pump long enough to verify a malfunctioning fuel pump relay not diagnose other issues. If you have power with the jumper in place the relay is the likely culprit.
Be sure to attach both leads directly to the positive and negative side of the fuel pump. Alot of people will use the chassis as a negative ground (-) which is fine in some situations but there are times when you lose the ground instead of the positive hot lead from the fuel pump relay. If you reference the chassis instead of the negative terminal on the pump you will get a good 12 VDC reading indicating a bad fuel pump when in fact it simply lost its ground. It's a good rule of thumb to reference the negative (-) to the device your testing no matter the scenario.
Hope this helps. If you can't find your models pinout for the fuel pump relay email model/ year and i'll find them for you. If you do need a relay don't get ripped buying local. Every store around here wanted $190 for the relay.....ouch! Try www.autohausaz.com
instead. Replaced mine for $90 since shipping is free for any item over $50. Most items are Bosch/Mercedes OEM parts not the reman junk at the local shops. Fuel pump local (reman off name) $236-Fuel pump from Autohaus (BOSCH brand new) $130. You do the math.