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Are you using the original cables to attach the starter/batter/solenoid? they could be badly corroded internally and preventing the current(creating a high resistance) to start. I know I had to replace the ground cable on my 92 that had about 12-16 inches of green corrosion under the cable shielding. If the starter tests OK, check the actual cables.
Ok so I took my meter and the battery was reading about 10 volts. Then I put the positive on the battery and the other on the cable that goes from the solenoid to the starter. Then I put the positive on the battery and the other in the boot from the ignition switch. All read right below 10 volts. Correct me if I'm wrong but it is a battery problem right either the battery needs to be replaced again or the connections on the terminal aren't very good. Btw the battery I just put in was used it came off my old silverado.
put the battery on a charger and see if it can be topped off. If not, like was said before, it may be a dead cell or just needs electrolyte replacement/water.