How full is your fuel tank? I think the diesel used the same defective design of transfer pump for the left side tank.

If at ≈ 1/4 tank add some fuel, also does diesel have a low pressure fuel test point under the hood you can test for fuel pressure.

The symptom your described pull two feet forward and it shut off exactly describes the standard symptom of a bad cam shaft sensor. When that's the case it will usually start right up. Crank position sensor is however mission critical and if that goes bad car will not start.

I'd wait to know about the 1/4 tank answer before digging deeper.

The key remote radio is a separate radio from the RFID type of function used for starting the car. A proper scanner will tell you which key number is detected by the car to confirm it's working. Also: codes?

__________________
2011 E70 • N55 (me)
2012 E70 • N63 (wife)