The pickup assembly doesn't even do anything until the engine is cranking. It will not cause a failure to crank.
I'm not a fan of removing parts for testing. Almost any starter will test good off the engine, even those with bad brushes or bearings, because there's no load on it. A free-spinning starter motor will draw as little as 50 amps. You need to test it under load when it will need to draw up to 300 amps to get started, and around 150 - 200 to keep cranking. That's where bad brushes will show up.
Generators need to be tested for full-load output current and "ripple" voltage. That will identify one bad diode of the six. With one bad diode the generator will only develop a maximum of exactly one third of its design rating and that's not enough to meet the demands of the electrical system under all conditions. The battery will have to make up the difference until it runs down. That's why I had you measure the battery voltage first. The test benches at auto parts stores aren't strong enough to run a generator at full load. They can only measure the output voltage, (electrical pressure). It has to be on the car to measure maximum current, (electrical flow). In most cases when the maximum current is low due to a bad diode the output voltage will still be near perfect, so you can get a false good result on a test bench.
Regardless of these test results, I'm still thinking about the symptoms that point to two different problems, but presumably related. Slow cranking points to a discharged battery or a bad connection / frayed battery cable. No-crank with no sound from the starter suggests a problem in a circuit other than the starter circuit and battery cables. Most commonly the neutral safety switch would be the main suspect. The no-crank can be partially diagnosed from the starter relay but you have to do it while that problem is occurring.
Tuesday, June 4th, 2013 AT 12:23 AM