Q: Car does not start. Starter was tested. Relays tested. Battery tested. Only thing I could find is no power on thin wire of starter

Hi. I have a 1999 AU Ford Fairmont Automatic. Recently I had issues where the car was struggling to start. If I turn the key there will be no ignition. You can just hear the clicking of the relays. Then after several minutes the started will start shuttering and eventually start up. The happened on several occasions. Then all of a sudden the car did not start at all. I removed the starter and had it tested. The brushes needed to be replaced, but after cleaning it was working again. The solenoid is also working fine. Then I placed everything back, but still nothing happened. All the lights on the dash, radio and other electrical components seems to work fine. I have tested the relays, fuses and the battery. I then tested the thick red power cable running to the starter and there was power, but the thin wire had no indication of power. What should I do next or test next? I am lost at this stage.

My car has 260000 miles.
My car has an automatic transmission.