Bad connection somewhere...
Check battery, terminal connections, ground, starter relay switch (also known as solenoid) and starter in that order. The clamp on with 2 bolts battery terminal ends are a know problem causer. Corrosion gets in the clamped joint and works its way up the wire under the insulation. Avoid them like the plague...
A voltmeter is handy if you are familiar with how to use it to find bad connections. Measure the voltage drop across a connection while trying to start the car: more than .5 volts across a connection indicates a problem.
See http://www.fluke.com/application_notes/automotive/circuit.asp?AGID=1&SID=103 for help for help troubleshooting voltage drops across grounds.
Voltage drop testing of grounds.
Use a Digital Volt Meter (DVM) to measure the voltage drop across a connection or wire. Adding length to the test leads may be required, and does not affect the accuracy of the test. Use 18-20 gauge wire for the test leads if you have to lengthen them.
1.) Most grounds use the negative battery post as their starting point.
2.) The voltage will be small if the ground is good: less voltage drop = better connection.
3.) Be sure that the power to the circuit is on, and the circuit is being used in its normal manner. For instance, if it is a light circuit, the lights on that circuit should be powered on.
4.) To measure grounds, place one DVM lead on the battery negative post and the other on the wire or connector that goes to ground. Place the other DVM lead on the wire or connection you want to test.
5.) Read the voltage drop: Light duty circuits (1-5 amps) should show .1-.25 volts. Medium duty circuits (6-25 amps) should show .25-.5 volts. Heavy duty circuits (26 amps up) should show .5-.75 volt drop. A voltage drop lower that spec is always acceptable.
The same testing proceedure works well for the positive side of the circuit too.