I assume you are talking about the fuel pump relay. I have repaired the fuel pump relay in my 84 500SEL by re soldering some cracked solder joints on the printed circuit board. It has been fine for the last 10+years. If you have fuel pressure to the fuel distributor when you jumper pins 7 & 8 then the car should start.
First, lets start with the cold start valve. It will only spray fuel while the starter is en gauged and the engine is below 16 deg C/61 deg F and it has fuel pressure. It gets its voltage from the start signal and its ground through thermo time switch which is located in the front of the intake manifold and close to the cold start valve. It has 2 wires. The thermo time switch will also limit the time the cold start injector will spray depending on the engine temp. I don't know your location but if the ambient temperature is above 60 deg F, the cold start valve may not come on at all.
The first test of the fuel distributor is to watch the air flow valve (big round plate just in front of the fuel distributor). Does it go down a little when you hit the starter? Let us know and we can go from there.

Paul

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84 500 SEL (307,xxx miles)