Q: New battery, car still wont start even with jumper cables.

If the battery is new and fully charged, and you turn the key to the "start" position and you hear nothing that means that either the starter circuit supplying the starter motor (ignition switch, wiring, relay, fuse, etc.) has a defect or the starter motor/solenoid itself is faulty. The way the two possibilities are distinguished is simply to check for power to the starter motor. If power is being supplied to the starter, and yet the starter motor is not working, then it is condemned and replaced.. If power is not being supplied to the starter motor when the key is in the "start" position, then the reason why has to be determined. In the case of no power, wiring faults could be an issue inasmuch as corrosion on starter circuit terminals or circuit connections could reduce the current available to the starter motor enough that the starter just won’t work adequately especially in cold weather when the demand on the motor is the greatest. Basically, you have to perform voltage drop tests along the entire circuit to ensure the circuit itself is in good condition. To resolve this issue, the recommended service is a no start diagnostic and the responding certified mechanic will quickly let you know of the root cause of the problem.