All power works but no turn over

1. Make sure car is in park, or if manual transmission, you have clutch engaged. Check to make sure no anti-theft lights are on.
2. Confirm that your battery is good and has the needed power to turn the engine over. (I replaced my battery today...I had lights, etc too) Try jumping the car and if it starts, you have a bad battery.
3. Confirm ignition swithc works. Turn it to position 1 and see if all lights on dash light up as normal.
4. If you hear a clicking sound when you try to start the car, it indicates a bad starter solenoid.
5. If none of these two items (and assuming cables are tight and good as you said), then the starter is probably bad.