if the starter pinion pops up but the starter doesn't turn then its most likley the starter solenoid contacts.
if it was the battery or cable the voltage at the starter solenoid would drop as the starter engages, and cause the pinion to drop down again, making the voltage rise again, causing the charactersitic click,click,click,click, you get with a flat battery or poor battery cables.
connect your meter from earth to the main terminal on the starter and check the voltage at the terminal when turned to start, if its 12 volts then check the terminal the other side of the solenoid where the cable goes into the starter itself, if thats not 12 v too then the solenoid contacts in the base of the solenoid are the problem.