This is an old post so I will add info for future users. It was stated that the car may start after 4 to 8 attempts. This is a sign of 2 possibilities, the first being that a loose electrical connection or contact has heated up enough to tighten the connection and allow more amperage through to the starter. The second is a bad starter, typically where the bushings inside are worn and the armature is dragging, once you click the starter enough times and the armature moves little by little to a good spot, it will start. Related to this movement can also be a bad armature/brushes contact, again once the armature moves little by little to a good spot, it will start. You typically will experience starter problems that get worse over time.
As others have mentioned, clean all connections and contacts in the starter circuit, battery terminals, main battery positive and negative (engine and chassis grounds) cables, control circuits such as the P/N switch (requires disassembly to clean), ignition switch (this portion is only used to start and requires disassembly to clean, difficult to do if needed), starter relay (just replace it, may be difficult to disassemble to clean and wont last long) and all wiring involved in all the circuits (not burned, corroded (green) connections, or hanging on by a thread). The starter body itself must have a clean ground contact to the transmission housing or the engine block, which ever its bolted to so the metal to metal contact must also be brushed clean.
Bypassing the circuitry and jumping the starter direct at the solenoid (for testing purposes) takes caution to not short anything out, this is what Autozone will do on the counter when you take the starter into them but an unloaded test is not the same as an on the car loaded test. Although they may see the problem if bad enough and your lucky.
For those people who wish to rebuild their starter, you will first inspect for drag marks internally and signs of worn bushings/bearings. If worn to this point, just buy a rebuilt one over the counter. If your brushes are just worn out, inspect all the little copper armature contacts to be sure they do not have deep grooves worn into them, they don’t look burnt and a little sand paper around the area can smooth things up a bit, anything worse, buy another starter. Replace all the items for the solenoid and contacts leading to the points. If you feel large parts such as the stator, armature, bushings, broken housings are needed, just buy another starter. CLEAN everything and LUBE where needed.
I have only replaced the solenoid contacts in many Honda and Toyota starters to fix this type of exact problem. Good Luck to all future starter problem mechanics.