i changed my starter today because the car wouldn't start. After changing, the car starts but now I have the red transmission malfunction message "gear can be engaged without depressing the brake..". The car now shakes whenever in park or I'm not moving. It runs nicely when moving though. Also it was done while it was raining

 

I'm confused. If the gear cant be engaged then how does it "runs nicely when moving".

 

That is actually a possible BMW error message. Normally, shifting gears is not allowed unless the brake is depressed.

OP, I would reinstall the starter again, thoroughly checking everything. The starter is in indirect contact with the transmission through the flywheel.

 

Your post suggests to me that your starter motor is not disengaging after you start your car.

This will cause the engine to run rough at idel because it cannot run freely being restricted by the starter making it seem that the engine is running rough.

Then when you power up the engine is just turning your engaged stater motor over quickly although you should hear a noise.

I would check you have fitted the starter correctly as suggested and if you have check that the starter is suited to your car

I think this is an easy fix but if you dont do it quickly you could burn your starter out or even start a fire.

 

I don't think it has to do with the starter itself or the fact that the starter momentarily engages the flywheel when starting. If the starter wasn't installed correctly, I think you would know that pretty fast.

You need to look at all the electrical connectors you had to undo. I'm betting one of them isn't plugged back in or isn't seated correctly.