No starter operation not working?

This is typical of worn contacts inside the starter solenoid, but since the starter is new, I'd be more inclined to suspect a piece of debris was stuck in there from the rebuilding process.

Also, it is not unheard of for the coil of wire in the solenoid to warp and cause the core to stick. That typically happens more when it's hot, but as I recall, I don't think you'll hear the solenoid engage at all.

Do you see all the lights that normally comes on when key at run position, also do you have an auto theft deterrent device?

Okay-have helper hold key at start position and look for power at the starter solenoid purple wire terminal-do you have it-if so replace the starter. If not check the starter relay/transmission range switch, ignition switch and fuses also see below

Have you replaced the starter? That is the most likely issue. I noted that you replaced the alternator and battery already.

Here is a link that shows in general how it's done:

https://www.2carpros.com/articles/how-to-replace-a-starter-motor

Here are directions specific to this vehicle. Note that the directions also cover diesel engines, but that isn't relevant for you.

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1997 Chevy Truck K 1500 Truck 4WD V8-5.7L VIN R
Starter Motor Replacement
Vehicle Starting and Charging Starting System Starter Motor Service and Repair Procedures On-Vehicle Service Cranking System Starter Motor Replacement
STARTER MOTOR REPLACEMENT
Gas Engine Starter Motor And Heat Shield

pic 1

Gas Engine Starter Motor And Heat Shield

pic 2

Diesel Engine Starter Motor Shield

pic 3

Diesel Engine Starter Motor

pic 4

Remove or Disconnect
1. Negative battery cable. Refer to CAUTION. See: Starter Motor > Service Precautions
2. Starter brackets and/or shields, if equipped.
3. Wires from the starter solenoid.
- Raise the vehicle and support with safety stands.
4. Two bolts and washers (where present) holding the starter to the engine.
5. Starter from the engine.

INSTALL OR CONNECT
NOTICE: Refer to "Notice". See: Starter Motor > Vehicle Damage Warnings
1. Two bolts and washers (where used) through the starter to the engine.
Tighten
- Mounting bolts (diesel) to 40 N.m (30 lb ft).
- Mounting bolts (gas) to 45 N.m (33 lb ft).
- Bracket Nut (diesel) to 8 N.m (75 lb in).
- Nut (diesel) to 8 N.m (75 lb in). Lower the vehicle.
2. Wires to the solenoid terminals.
3. Brackets and/or shields, if equipped.
Tighten
- Heat Shield bolts (diesel) to 17 N.m (13 lb ft).
- Heat Shield bolts (gas) to 12 N.m (9 lb ft).
4. Negative battery cable.

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Let me know if that takes care of the problem. Also, make sure the heat shield is in place on the starter. Without it, the starter will get extremely hot from the exhaust system and can cause what you experience.

Take care,
Joe

I would suggest ruling out a fuel issue when this is happening because a hard start when hot is normally due to low pressure.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

It may help if you got a recording of the truck trying to start to get us all on the same page. Thanks