Your 129 has 2 fuel pumps with check valves along with a fuel accumulator. The setup is located just forward of the rear wheel, passenger side underbody, under a black protective cover.
You can test to see if both pumps are operating by pulling the MAS relay and checking amp draw between big pins 1 and 2. Proper specs for 2 pumps is 6 to 7.5 amps.
Not sure if the early 3.0 104 engine has an OVP or not, but I suspect it does. Most likely located behind battery on passenger side.
Another suspect could be the fuel pressure regulator or old fuel filter.
'01 E430, Sport 72,000 mi
'98 C280, 126,500 mi