Your crank cannot be broken. The starter turns the rear of the crank, the timing chain is off the front. So if you have a broken crank the cams won't turn. Look for the cheap & easy stuff to fix before you conclude that the engine is toast.
Anyway, I'm not sure I'm totally clear on this. The engine will spin (I call that turning over) but not fire up (I call that starting), right? Like the starter is spinning the engine properly, just no start right?
If I'm right, and it's an E30, check & clean the crank position sensor, main & pump relays and maybe the fusible link in the trunk.
Fix the vac leaks, they will stop the car from running...and loose/corroded/broken wiring or plugs. If you have a US spec car, do you get a Check Engine light? Do you know how to do the stomp test to get the OBD codes?
If it's an early e36 ('93-'96), check the aboove problem areas and also the ECU compartment for water or a plugged drain. Especially if it rained recently, or did you have a really good high-pressure car wash?
BTW, welcome to the board...even if you're here out of desperation! We'll get you running. Please post your car's year type & model. FYI, I have a '91 e30 318i sedan. It makes a big difference to figuring out the problem. Use the search too...every problem you're likely to have with this car is discussed on this board...and many more besides!