Being a 2001 Model year it should be MEMS 3 and EWS.

It seems to me you have over looked the most plausible reason. I would say the MEMS unit is still in a immobilised state. (injection is blocked)

You will need T4 or Autologic to perform the immobiliser relearn function first.

EWS is a BMW system and can be prone to loosing sycn with the MEMS unit. (check battery voltage during cranking)

Synchronize with engine management system This function causes the immobiliser ECU to send out repeated codes so that when used in conjunction with the LEARN feature on the engine management ECU, that it can synchronise itself to the EWS 3D immobiliser.

The function should be used only after setting the engine management ECU in learning mode.
The synchronization procedure is done in three steps that should take place in one ignition cycling.

Put the engine management in learning mode: This function is to be found in the engine management START SYNCHRONIZATION WITH IMMOBILISER ECU. The function will set the ECU into learning mode.

Once you've been prompted that the engine management is in learning mode, navigate to the immobiliser for step 2.

Send code from immobiliser ECU: This function is to be found in the immobiliser. This function will send codes to be learned.

Once you've been prompted that the immobiliser sent the code successfully, navigate back to the engine management for step 3.

Take the engine management out of learning mode: This function is to be found in the engine management END SYNCHRONIZATION WITH IMMOBILISER ECU. The function will end the learning mode, leaving the ECU in normal mode