Check if battery is charged o rule out bad battery. A good voltage while the car is off and has not been running for a few hours (idle voltage) is ~>=12.8V. Anything above 12.3 V is okay. Does any other high current load work well (headlights, rear defrost, fans .. while the engine is not running? What happens when you turn the key? Do the dashboard lights stay bright ? Is there any noise indicating the solenoid engages or starter try to turn ?
Rule out faulty relais, fuse, voltage drop on cables, conenctors etc.: Check the voltage on the solenoid itself while you turn the key to crank. If the voltage is close to the idle voltage the solenoid does not engage.