The car will start if you hold the key inthe start position

indicates that the power to the stop solenoid is not working or the stop solenoid has failed and switches off in the run position

I had this exact symptom on my 1984 533i. I spent months diagnosing everything but the computer. It was the computer that failed. Actually only part of the circuitry failed and is probably repairable. When the car is cranking it would run. I set up a wire harness that allowed me to shut off the starter motor while I was holding the key in the starter motor position. The car ran just fine. The 533, 633 and 733 all use the computer ending with 008. DO NOT slap in any other computer unless you actually know what you are doing. I tried. And you risk damaging good components, like the donor computer and the injectors.

Does the car have a factory security system? it may have a starter kill on it.
also check for voltage at the starter solenoid while someone holds the key to start position, you could have a faulty ignition switch.
the engine light stays on when the key is on until engine starts.

EITHER CRANK SHAFT POSITION SENSOR OR ITS THE CAM SENSOR. IF YOU CAN FIND SOMEONE WITH A CODE READER FOR YTHE COMP. AND THE COMPUTER WILL TELL YOU EXACTLY WHICH ONE IS NOT FUNCTIONING CORRECT

This can be caused by many things. The most common is an intermittent connection to the Crankshaft Position Sensor or the sensor itself. Find the wiring harness to the sensor and wiggle andpull on the harness with the engine running to see if you can make it die. If it dies, you probably need to fix the wires inthe harness. If you can't make it die, let it run for a while and see if it dies on its own. If it will die while just sitting there idling, replace the sensor.

replace the ignition starter switch, this switch is attached to the back of the ignition key cylinder, this a very common issue on your car. remove the **** shell covers of the column to access very easy job here is the part number and price.
ACDELCO Part # E1463 Price $46.79

Inside engine compartment, look for injection pump, on side or top you will find an electrical connection, that connection comes from Your Key, it is an on and off electric valve, if You bring 12V power strait from the battery and clip it to that valve, go and try starting car, if car runs, after Your key or a Relay, my be defective, look for oil and coolant level, and Diesel Filer

You are gonna need a New Ignition. Will solve this Problem.

sounds like you have a bad ignition switch they were good for it

Does the engine die as soon as you release the key, or does it run for a couple of seconds after you release the key and then die? If it dies as soon as you release the key, try holding the key for a few seconds and see if it will stay running as long as you are holding the key (the starter will make a grinding sound while holding the key but won't hurt anything). If it stays running while you hold the key then dies when you release it, that indicates that the ignition switch is bad.