Q: car won't start: electrical problem

Even a relatively new battery can be bad. If it has an internal short, a jump start may not even work to start the vehicle. try removing the battery and taking it to a local auto parts store, or where it was originally purchased, for a load test, not simply a voltage test. If the battery tests good, then the problem is elsewhere. It could be a bad starter. If the internal windings of the starter have a "dead spot’< then power will not be applied to the starter motor to crank the engine. Also, other components can be effecting the signal to the starter. The ignition switch may not be signaling the starter relay to provide voltage to the starter. The relay may be receiving the signal from the ignition switch, but may not signal the starter to power up. Also, depending on the type of transmission, things like the neutral safety switch, or clutch pedal safety switch may be shorted. Either of these will prevent a signal from reaching the starter.

Since replacing parts at random can get quite expensive, have a certified technician look into the no start condition to isolate the exact cause.