1. Check the obvious:
* Ignition Switch: Try wiggling the key while turning it. A faulty ignition switch can prevent power from reaching the starter.
* Starter Relay: This small electrical switch is often located in the under-hood fuse box. A bad relay will prevent power from reaching the starter motor. You might be able to hear a click from the relay when you turn the key if it's failing intermittently. Try tapping it gently (with the key off) to see if that helps temporarily.
* Fuses and Relays: Check all fuses and relays in the under-hood and interior fuse boxes. Look for any blown fuses (broken filament).
* Neutral Safety Switch (Automatic Transmission): Make sure the transmission is in Park (or Neutral if it's a manual). A faulty neutral safety switch will prevent the car from starting.
* Steering Wheel Lock: Sometimes, a stuck steering wheel lock can prevent the car from starting. Make sure the steering wheel is not locked.
2. More involved checks (requires basic mechanical knowledge or a mechanic):
* Starter Motor: This is the most likely culprit if the above steps don't reveal anything. A failing starter can make a clicking sound, grind, or do nothing at all. Testing the starter requires some electrical knowledge and tools (multimeter). You might need to remove it to test it properly.
* Wiring: Check the wiring from the battery to the starter, including the positive (+) and negative (-) cables. Look for corrosion, loose connections, or damaged wires. Clean any corrosion you find.
* Solenoid: This is part of the starter motor. A bad solenoid won't engage the starter motor even if power is reaching it.
* Ignition System: A problem in the ignition system (distributor, ignition coil, etc.) will prevent spark and thus won't allow the engine to start. This is less likely if everything else electrical is working.
3. Get Help:
* Jumps start: Even if you replaced the battery, try a jump start. Sometimes a new battery can have a faulty cell. A successful jump-start confirms a problem with the battery or charging system (which you ruled out).
* Mechanic: If you're not comfortable with these checks, take it to a mechanic. Diagnosing starting problems requires experience and the right tools.
Important Safety Note: Always disconnect the negative (-) battery terminal before working on any electrical components in the vehicle. Failure to do so could lead to injury.