Restarting Chrysler 300 after radiator leak and engine stop

how long did the car run without fluid in the radiator? You may have seized the motor... and being as I just completed a radiator/waterpump/t-stat/radiator fans on a 2006 2.7L 300- I can guarantee that motor will fry itself quickly if there is no fluid in it.

The engine is soft because I already turned it with a tool by hand

Does the engine crank, when you turn the key? if not, then you have a starter issue- which is largely unrelated to the radiator leak.

When I turn the key the engine doesn't turn but the starter makes a whistle noise on the starter not on the engine

whistle noise? you mean at the ignition? That's the fuel pump- when you turn the key does the motor crank?

When I turn the key the stater does make a noise, not the engine

Im stymied by your descriptions-- Im sorry brother--- replacing the radiator on your car has nothing to do with the car being able to start. You say the starter makes a noise when cranking the car, a 'whistling' noise as you put it, but starters don't make 'whistling' noises. Perhaps the battery is dead, or doesn't have enough juice to spin the motor- however, I am at a loss. Anyhow good luck with the repair.