Starter doesn't catch - 1998 Chevrolet S-10 Pickup

Very good chance that teeth are missing from the fly wheel. Remove the starter and inspect the teeth of the flywheel

On top of your starter is a "solenoid", which does two jobs:
1. it's the starter relay,
and
2. it engages the pinion gear on the starter with the flywheel.
There is a "bendix spring" that retracts the gear when you stop cranking. The gear can get stuck on the shaft, and the starter will just spin....

solenoid isnt working have starter checked

It would help to know what kind of "won't start" you mean. Is it just ticking? Low battery voltage. Considering it started after getting your phone, probably not that. Is it cranking slow and not trying to catch (where it spins faster as the engine is firing but not fully catching and entering a run state)? Is there nothing at all, just shuts the accessories off and does nothing, no click, tick, hurk, jerk?

I had a Malibu that did not like starting too fast. As in if you flipped the key switch straight to start the fuel pump wouldn't pressurize properly or something. But if I turned it to on, gave it a second (you can usually hear when the fuel pump stops running once the system is up to pressure) then hit the starter it kicked over just fine.

If you have tested the starter, and it is installed correctly, and it spins, my guess would be missing teeth on the flywheel.
A Ford starter needs 11 volts to engage so you could check to make sure you have that at the starter cable post.
You could also turn the crank a few degrees to see if the flywheel is warped or damaged.

I don't know beans about automatice transmissions and the average person can only check the fluid levels and take it to a transmission shop if it is more serious.
As far as the engine goes, you need to localize the problem because with the other indications it might not be the normal stuff. So, what I would recommend is that you take the serpentine belt off and try to turn the crank with a large wrench (CW only) with the car in neutral. If you can turn it, then it is probably not your engine freezing up. If it won't turn then the transmission is probably not disengaging from the flywheel - maybe the torque converter.

If it does turn over, then you can put the belt back on and try to jump start the car with another vehicle or the boost function on a battery charger. It it starts then you know to look at the charging system - battery, alternator. If it doesn't start then the starter or the starter reley.

Count the teeth of the starter the teeth of the starter is different you will need to disasemble the starter and change the teeth over some have 9 teeth and some have 11 teeth

The starter is at the very back and bottom of the motor just infront of the transmission. This sounds like a starter seliniod failure

Sounds like a Bad starter solenoid or the Starter has come loose and isn't catching the flywheel correctly.

1- If engine is not cranking but hearing a click then

a- Problem with battery.

Try to jump start then if battery is over 5 years, replace battery

b- Solenoid works but not the starter.

Need to repalce the starter.

2- If engine is cranking but not catching on, then the problem is with the Bendix part. it is an intergrated part of the starter.

Replace the starter.