So I pulled the starter and took it to a parts store and bench tested it. It passed. It put a volt meter on the solenoid wire and turned the key to the start position and got 11.6 volts down the solenoid wire. When we tried to start it the first time it sounded like the teeth of the starter hit the teeth of the flex-plate incorrectly and didn't engage. Then the solenoid retracted and made the whizzing noise that they make when they've gone bad. The next time we tried to start it it just made the sound like the solenoid had gone bad. I pulled it. It has a lifetime warranty, so I took it to the parts store to get a new one. They tested it and it passed. I didn't trust they're test, so I took it to an independent parts store and they tested it and it passed again.
This morning I tested the solenoid wire, but to me it checks out, so I'm lost as to what to do next.

so I went ahead and put the starter back in and it started right up. I shut it off and started it up a few times no problem. I'm stumped?

Update: Today I drove it to the doctor's office. It started fine when I left. After I got done at the doctor's office it made that whizzing sound like the solenoid isn't engaging. I tried it a couple more times and it started.

 

What brand starter?

I remember years ago I got a starter for my old Dodge Dart and it would fail now and then. I got really good at replacing it and being a college student I was on a budget. But eventually I got tired of doing that and got a better made one. You might be in the same situation.

 

It's re manufactured, but I'm almost positive it's not the starter. I just watched a YouTube video about diagnosing starter problems. It showed how to test for to much resistance in my positive battery cable. If it had to much resistance that would reduce the voltage going to the starter. I think I'll check that next.

 

My money is on a bad starter...

 

Measure the voltage at the started threaded lug during cranking. If the resting battery is fully charged to around 12.5V then during cranking at the starter you should see 11.0V +/- 0.5V. If you have an amp clamp meter put that on the main battery cable and during cranking look for 100+ amps or at least a lower range is pegged.

Trying to draw final conclusions with cable resistance measurements is dicey when the system needs to draw 100+ amps.

George