Weird starter issues even after replacement
Quick story of the circumstances...Went to start my car after work and it did absolutely nothing. Battery is in good condition, all other power works (windows, A/C, headlamps, stereo, etc...) but when I went to start it, nothing. So I assumed the starter had failed. Knowing you can get a few more starts from whacking it with a wrench, I jacked my car up in the parking lot and gave it a few light smacks. I went to start it and VIOLA, it worked. I assume it is for sure the starter so I purchased one from NAPA (reman). I go home and install it and still nothing. The issue still exists and when I turn the key, nothing happens. Still have power to everything and the battery is still good. I take the starter back to NAPA thinking it was a dud, they bench test it and it works just fine. I get a different one from them just in case (also bench tested successfully), install it and still have the same issue. Except this time, I turned the key 3 times with no success and on the 4th time, it started right up. I turn it off, then start it again, turn it off, start it again....so it seems to be working... I go to lower the car back down, and get everything back to normal and try to start it once more and it cranks 1 time and then stops cranking completely. I keep trying to turn the key and crank it and still nothing. I keep trying and then it works again for a few more starts, one after another.
I now proceed to diagnose knowing I have a god starter and battery. I measured the voltage at the power wire that connects to the starter and it is reading battery voltage (no voltage drop at all). I went to measure the voltage at the power wire to the solenoid but I couldn't seem to get anything from it. I'm wondering what conditions give this wire power? I tried measuring it with the key turned all the way on but I'm not sure if this is the correct configuration to get power to that wire...maybe this not having power is the issue? Where does this wire run to (I'm assuming to the relay)?
I then started swapping the starter relay with the Hi and Low headlamp relays. When I swapped them the issue was still present and with the starter relay in the headlamp socket, it worked normally. So right now I am at a complete loss and looking for guidance. What would cause this issue? I assume its related to something in the starter circuit and I'm hoping someone here knows a few more tests I can try with the wiring to diagnose if I have a bad wire or fusible link (if one exists in this circuit). Could this be non-starter related also?
Thanks in advance for all of the help!