When your car acts up, diagnosing the actual root of the problem can often be very difficult, as many parts are meant to work together in order for the engine to start and run properly, and for you to control the car when braking, and the like. What also makes diagnosing a problem difficult is that some mechanical issues can actually be traced to electrical problems under the hood, and are not the fault of a failing part itself. Note a few of those issues here so you can know when your car may need an automotive electrician versus a mechanic.
A dead battery is the most common electrical issue that could keep a car from starting, but the starter motor could also need electrical repair work. This motor is what actually turns over the engine in the car when you turn the key, meaning that it gets the pistons moving. Since the starter motor runs on electricity, if it has bad wiring or if there is a blown fuse or blown circuit to the starter, this motor may fail to operate. In turn, the engine won't start, even though the battery itself may be fully functional and charged.
Most cars today have an anti-lock braking system, or ABS, installed; this system will usually vibrate or pulsate the pads just slightly as they close against a rotor, so the tyres can maintain their grip on the road during a hard brake, rather than the car sliding around and skidding to a stop. The ABS system is also an electrical part; if it has worn or bared wires or an open circuit, you may notice your car skidding around and becoming difficult to control every time you touch the brake pedal, even though the pads and rotors may be fine.
If your key fob doesn't open the power locks on the doors, this could be a low battery in the fob. However, note if the power switch on the inside of the door also works to unlock it; if not, this usually means there is an electrical problem inside the car itself. The wiring to the locks or junction box that connects all the wires in the door to the car's electrical system and computer may have become bare and frayed. A blown fuse or circuit can also interrupt the power to the door. Replacing these can get the key fob and switch working again.