Hearing the pumps run is certainly a good thing, but that doesn't mean the fuel pump relay is good. One symptom of a bad fuel pump relay is stalling at anything but idle in a KE-Jetronic system. Obviously, the car needs to have been started for this to happen.
If you suspect a fuel pressure/delivery problem, you need to hookup a fuel pressure gauge. Anything else is just guessing.
Personally, if the car is not starting, I'd check the ignition system first. I'm assuming that you've already done that.
1988 560SL Black/Palomino
1988 300SEL Black Pearl/Burgandy
1984 500SEC Anthracite Grey/Palomino