When I turn the key the car will not start but I could listen the radio?

Your car has several different ignition positions. They each offer slightly different functionality.
Off: In this position, the engine is off, and so are your electronic accessories (unless the delay has not expired yet). You can still turn on lights (headlights, interior lights, etc.).
ACC: This is the accessory position. Turn the key to ACC if you want to listen to the radio, play a CD or use other accessories without cranking the engine.
On: In this position, all of the electronics should come on. This is also the position that the key will return to after cranking the engine.
Start: Turn the key to this position to crank the engine. Let go of the key when the engine is running and the key will return to the on position.

http://www.aa1car.com/library/ignition_switch_positions.jpg

I use to own a car that had an ignition that was ACC - OFF - ON - START.

Try turning your ignition one position clockwise and see if the radio turns off and the key comes out.

https://hackadaycom.files.wordpress.com/2008/08/ignition.jpg?w=450&h=338

Can you have someone listen down by the starter when you turn the key to start to see if they can hear anything that sounds like a wrrrr ?

The ignition lock is malfunctioning. It's in the steering column

Sounds like you have an electrical short under or inside the dashboard somewhere.
PLEASE do not turn the radio on again until that is fixed.
As a retired firefighter, I can honestly tell you, you might start a fire and burn up your car if you do not fix this.
Be blessed.

Hook a charger up overnight, or try the jumper cables again. Make sure they are connected to the matching terminals. Check to see if anything has power without starting the car. Lights or radio working with key in the ACC position? If not, something has killed power from the battery- maybe a main fuse or a power distribution relay. Make sure the cables/connections aren't corroded at the battery posts.

Did you replace the key switch or the ignition switch behind the key switch?

flat battery activates the anti-theft code for the radio
you will need to get it and put it in the radio for it to work

The radio has two power wires and one is for the memory.

Try cleaning the fuel filter. listen for a whirring noise from the fuel pump when you turn the key.

you may be out of gas or have a bad fuel pump