Inspect the Electrical System
The newer your car the more electrical components you'll probably find under the hood, but even old engines can have electrical problems. If all the mechanical parts seem to be working properly and you still can't start your old engine, you may have an electrical problem.
The easiest problem to diagnose and fix is the battery. Car batteries are made up of a lead-acid or lead-calcium system that converts chemical energy into electrical energy. Batteries go through a recharging cycle when the alternator sends a current to the battery's internal plates and back into the electrolyte mixture inside the battery.
When a battery isn't being used, the chemical reaction in the battery breaks down and causes it to lose its energy. If the battery sits long enough it will be ineffective for starting up the engine. If the battery isn't that old, and it's a maintenance free model, you may be able to add a little distilled water to it to see if you can generate the charge. If it's been sitting unused for a really long time, it's best to install a new one.
In addition to checking the battery, inspect the ignition coil and coil wire. Use a multimeter on the coil to see if the resistance reading matches the recommendation for your vehicle. If it doesn't, then the coil may be bad. If the coil and its wiring work, use a current reader to see the starter motor is receiving a current. Corrosion or bad wiring can inhibit the starter motor and prevent the engine from firing up.
If your electrical systems are working and the car still won't start, you'll need to try a different approach.