Car will not start intermittingly

Your saying the starter won't crank? What is litre size of engine? W/wo trans control module? When the problem occurs, can you tell if there is a load on the starter circuit? Check starter circuits, Clean all grounds? Make sure the starter mounting surfaces are clean. You could even use a jumper ground from starter motor housing to frame, to see if it helps? I'm not talking about the mounting bolts.

You need to make sure the battery has a full charge. The generic spec for a full charge is around 12.6 volts Use a digital multimeter across battery posts when the problem is ongoing, have a helper turn key to crank, what is the reading? If load on starter, reading will probably drop to 9 or 10 volts. You have to test when problem is ongoing.

Is this an automatic? When problem occurs, did you try cranking in neutral? The diagram below is 6 cylinder with tcm. At the relay top, red wire is hot all the time, yellow wire goes hot with key in the crank position. The ground for control side of relay, is through the neutral switch. No ground or voltage and the relay won't energize.