Crank, no start

How close is the replacement engine year wise? Some of the companies made a lot of changes in that era and entire engine control systems and engine hard parts were different. The engines would bolt in and appear normal but because of the changes they won't ever run.

Another possibility is that the battery disconnect may have triggered the built in security system and tripped the immobilizer which shuts off fuel and spark. On some of them you can reset that yourself.
https://www.2carpros.com/articles/how-to-reset-a-security-system
On others you need a good scan tool to do the reset.

The only other item may be that you have to do a reset on the ECM so it can see the new crank sensor.

For most of them you do the reset for the sensors with a good scan tool, not the code readers that they use to scan for free. I actually try to avoid BMW and Mercedes because they don't really use a uniform diagnostic from year to year or even model to model. They also seem to think that if having one wire and a solenoid to do the job is good, replacing that with two control modules that you need to use a scan tool to access is just right.

OK it's a 2003 C320 Coupe, Sedan, Wagon? With All Wheel or only rear wheel drive?
Those are different going by Hollander. At least it may point out that you have a "correct" engine.

OK, they show the SLK 320 as using the same engine, so it should be correct.

I doubt the ECM is bad. It sounds more like a security issue. Might be worth it to get it to a dealer and have them do a full scan and make sure the ECM is OK and they can look at the system and see if it is a security issue.