this story will make you feel a little better
(I have already posted this, maybe even here, forgive me)
In college, many years ago, when crude oil walked the earth in the form of dinosaurs, I had a 1972 SAAB 99 (I was older than my car by only a few years, however).
Anyway, one afternoon, while futzing with the car, I found this really ratty piece of cardboard or fiberboard under the exhaust manifold. I was like, "I don't need this crappy thing" and ripped it out, threw it away.
A few weeks later, my car wouldn't start. I already had an alternator issue, and had replaced the alternator brushes (incorrectly as I later found out), and also replaced the battery (the regulator had an appetite for batteries) earlier so I was like, wtf.
I went on a fruitless thing, and even jump starting the car wouldn't work, so I push started the car, drove to napa, double parked, and bought a bosch starter.
Several aggravating hours later (I was doing this work with like, handyman drugstore tools) I got the new starter in and voila! IT WORKED! I WAS A GENIUS. Even my girlfriend at the time was impressed (didn't last long).
So, a few days later, new starter, new battery, new regulator and brushes. I drive to the store, get a case of beer, come out... CAR WON'T START!
All the same symptoms... jump no worky, push start, drive home. My friends are like, "well, maybe you got a bad starter..."
So, I rip the starter out (faster than the install haha), take it back to NAPA, they cheerfully exchange, I reinstall. and then... it WORKS!
Problem reappears a DAY LATER!
longest story short -> that crappy fiberboard thing was an asbestos heat sheild, and I was cooking solenoid after solenoid
so, don't feel so bad. It took me 3 starters before I realized it wasn't the starter.