Hi, I haven't got any details of what vehicle as yet, I will try to help with what I know so far.
In summary, you have a good battery now on the vehicle, however when you turn the key all you hear is a click still.
As you can hear a click, it is likely that the immobiliser system if fitted is okay and the signal is being sent to the starting motor, the solenoid is most likely the sound you can hear.
Either the solenoid doesn't have it's heavy power supply feed from the battery, or more usually the solenoid has failed, you could use a simple 12 volt bulb and a piece of wire to see if there is power to the solenoid, it will be the largest and heaviest wire to the starter motor, it will be permanently live with the battery connected, if the power is there and the battery is good, then yes, it is likely you will need to look at the starting motor.
If it is a manual, try rocking the car in gear, on the very rare occasion this helps and it would seem you have nothing to lose trying.