Why does my car not start with a brand new battery?

Could be,The new battery is discharged.

The battery cables are faulty or corroded.

The starter is faulty.

The starter solenoid is faulty.

The starter relay is faulty.

The neutral safety switch is faulty.

The ignition switch is faulty.

If the starter is cranking the engine but the engine fails to start and run there could be many more reasons. Give us more details.