Changed battery now car will not start

First clear something up. First you said the engine will not start, then you said it runs a while after removing jumper cables. Were the jumper cables involved in a different problem before the crash? If so, that points to a charging system problem that we will need to address after the running problem is solved.

Sorry to be the bearer of sad news, but BMW is one of the worst manufacturers, followed closely by VW, Audi, and GM, at purposely designing in tricks to force you to go back to the dealer. One of those customer-unfriendly business practices is the warning against disconnecting the battery. You must use some type of memory saver device that keeps the electrical system live while the battery is disconnected and/or removed. Once power is lost, a number of computers will lock up and can only be unlocked by the dealer.

We have all heard horror stories, mostly about VW's and BMW's, that if the engine does start, it will only idle and will not come out of park. Pressing the accelerator pedal does not raise engine speed. You have to drag the car off the hoist and skid it out of the shop to load it on a flatbed truck to take it to the dealership. My understanding is a $900.00 bill is not uncommon, but I really hope you come back and tell us it was not that bad.

To add to the misery, BMW is extremely selfish when it comes to sharing repair information and paint codes with independent repair shops. I do not have any wiring diagrams for your starting or charging systems from our normal sources. That adds another level of frustration.

I was able to find a wiring diagram in Mitchell ProDemand for your starter system. It shows an "Electronic Vehicle Immobilizer" module as part of the control system. It appears to have five wires in an eight-pin connector. You might find it only has four wires. The location of this module is not listed, but logic would suggest it is under the hood. You will need to list the engine size and transmission type if I have to look at more wiring diagrams. I used one for a 2.5L engine for the following:

Terminal 1 is a black wire. It feeds 12 volts to the starter solenoid during cranking.

Terminal 2 gets the 12 volts from the ignition switch when it's in the "crank" position. That's a black/blue wire.

Terminal 4, black/violet, gets a signal from the "Digital Motor Electronics Control Unit" listed as "left rear of engine compartment". That would be part of the anti-theft system.

Terminal 6, brown / black, comes from the "Transmission Controller" if you have an automatic transmission. Cannot tell if that is a ground signal, voltage signal, digital signal, etc, from the diagram. If you do not have an automatic, then, ...

Terminal 8, a blue/black, gets grounded by the clutch switch.

Interestingly, there is no separate ground or power feed wires shown for the immobilizer module. I suspect it gets powered up through the ignition switch when it is in the "crank" position and the ground would be provided through a neutral safety switch circuit in the Transmission Computer, or through the clutch switch.

A starter solenoid can draw up to 20 amps, and while a lot of import cars handle that high current through the ignition switch, that is a real lot to expect of those tiny contacts. More commonly there is a starter relay involved to handle that load, and I am wondering if there is such a relay inside that Immobilizer Module. Terminal 1, the black wire, is going to be substantial, as in fat, because it definitely is carrying the high solenoid current. Look for another wire on that module that is just as fat. That will be the 12 volt supply wire. If you jump those two together, the starter should crank the engine, but be careful as that will bypass the clutch switch or neutral safety switch circuitry and the engine will crank in gear. I do not want to read that your neighbors were laughing at you as you chased the car down road!