There are a couple of things I can suggest. First of all, fuel pump relays on all cars will never turn on continuously with just the ignition switch turned on. To do so would create a serious fire hazard if a fuel line got ruptured in a crash. With a damaged fuel line, the engine can't run without fuel pressure. When it stalls, the Engine Computer sees the lack of rotation, so it turns the fuel pump relay off. My reason for mentioning that is you can have a problem with one of the two sensors the computer looks at to determine if it should turn the relay on. Those are the crankshaft position sensor and the camshaft position sensor, or whatever name the manufacturer gives them. If you have a distributor, the camshaft position sensor is usually inside it.
Those sensors are also what is used to determine spark timing. A failing sensor can cause erratic loss of spark and / or backfiring, and it can cause the computer to intermittently turn the fuel pump relay on and off. Replacing the relay can result in the illusion something has changed when the real cause is related to those sensors.
(Looks like you're in the Central time zone. So am I).
Since your engine uses those sensors, there is going to be an Engine Computer involved, and that usually means the ability to detect problems and set diagnostic fault codes. We have listings here for those codes and how to read them, but I don't see anything for Mercedes. For '96 and newer cars, most auto parts stores will read the codes for you for free, if you can get the car there. For '95 and older models, scanners specific to the vehicle brand are usually needed, so that means making a trip to the dealer, or buying your own scanner. I have a number of scanners that work on Chrysler vehicles, and you can find those on eBay for as little as 50 bucks.
Reading those fault codes is the place to start. They never say to replace parts though, or that one is bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition. When a sensor is referenced in a fault code, it is actually the cause of that code about half of the time. You also have to look for cut wires, bare wires that are grounded, stretched connector terminals, corroded splices, and things like that.
Don't overlook a jumped timing chain too.
Wednesday, September 24th, 2014 AT 10:27 PM