For how long do you have the new battery? It is clear sign that there is no enough power to start the engine. Meaning, flat battery, or loose connection on power cables. First is easy to chek with multi meter. Chek the voltage with it, should be over 12V. If yes, turn on ignition and turn on all lights, fan, radio, leave door open. Chek voltage now. If it drops below 10V and more - flat battery. Try to recharge it. Also chek for charging voltage when you manage to start the car. It should be 13.5V and more. If it isnt, then alternator problem or again, loose cable in the system.
If voltage remains on 12V when all consumers are on for few minutes then - loose cable problem or starter problem.
Third thing can be that something is draining the battery when car is not runing. When key is out of ignition, only radio, cabin lights, and remote lock should have power. Usualy, when some aftermarket part is installed POORLY in car, like new radio or allarm system, then battery drain errors occur.
