I agree, you can get corrosion inside the battery cable and cause the voltage/amperage to get through.
Get a volt meter and see if there is any voltage drop o difference between the battery post and the clamp and then again between the cable at the starter and the started post. The voltage should be the same.. at every point. If not YOU have found your problem.
Make sure you check the ground cable as well. All the same problems could be found here AS WELL as paint on the block were the ground is attached........It is attached to the block right?
