* Low voltage: While you say the battery has *lots* of power, a slightly low voltage can still cause the solenoid to click repeatedly without enough power to engage the starter motor. Have the battery and charging system tested at an auto parts store (they'll do it for free). A weak battery or alternator can cause this, even if the battery seems okay at first glance.
* Bad battery cables or connections: Corroded, loose, or damaged battery cables (positive and negative) can prevent sufficient current flow to the starter. Check these for corrosion, looseness, and damage. Clean the terminals thoroughly with a wire brush and baking soda if necessary.
* Faulty starter solenoid: The solenoid is the electrical switch that engages the starter motor. If it's failing, it might click but not fully engage. This is a common failure point. Replacing the starter solenoid is relatively inexpensive and often fixes the problem. It might be easier to just replace the entire starter motor as a single unit.
* Faulty ignition switch: Though less likely, a failing ignition switch can prevent the power from properly reaching the starter solenoid.
* Neutral Safety Switch (NSS): Your car likely has a neutral safety switch that prevents starting unless the car is in park or neutral. A faulty NSS won't allow the starter to engage. This is a common issue and inexpensive to replace. Check that your car is in Park (or Neutral if it's a manual transmission).
Troubleshooting steps:
1. Battery and Charging System Test: This is the *most important* first step. Get this tested professionally.
2. Check Battery Cables and Connections: Inspect for corrosion, looseness, and damage. Clean and tighten as needed.
3. Try tapping the starter: (Use caution, the starter is hot when running) Gently tap the starter with a hammer or wrench *while someone else tries to start the car*. This sometimes temporarily fixes a problem with a sticking solenoid or worn contacts, but it's not a long-term solution. If this works, it points to a starter or solenoid issue.
4. Check Neutral Safety Switch: Make sure the gear shift is firmly in Park (or Neutral). If you suspect the NSS, you may need to test continuity with a multimeter, or simply replace the switch (relatively inexpensive).
If the battery and charging system check out, and you've checked the cables, the next step is likely to replace either the starter solenoid or the entire starter motor. Given your description, a replacement starter is the most probable solution. If you're not comfortable working on cars, take it to a mechanic.