You can somewhat diagnose a no crank by observing the dome light (assuming it works) while attempting to crank. If the dome light doesnt go out, its safe to assume the battery/connections are good enough that the battery is charged and the starter isnt pulling any current. If the dome light goes dim, the battery is weak or there is excessive voltage drop in the circuit. If the dome light goes out, the battery is DEAD, or there is a LOT of voltage drop. If the light comes back on after a few secs, typically you have a bad connection in the cable at the batt.
BTW: no, you cant use the radio display, because the ACCY circuit is turned off at crank. You can however use the headlights if the dome light is inop...if you can see them.
ie:
turn the key, hear a click, dome light stays on, typically the starter motor isnt pulling any current, but the solenoid is engaging, the solenoid "jumper" piece inside is corroded/burned, or the starter motor brushes/armature are bad.
turn the key, hear click, the dome light goes out, release the key, the dome light comes back on, the batt is dead/weak.
turn the key, dome light goes out, release the key, dome light stays out. Wait a few secs/few mins, the dome light comes on as bright as before: bad connection...typically pos lug at the battery, or cable corroded in its casing.
Turn the key, cranks slowly, dome light doesnt go out/dim: starter is bad, or excessive voltage drop in pos cable (depending how the car is wired. On a GN the starter would be bad. ON a 90's C/K pickup, I'd say wiring prob. (C/K pickup splits the pos cable to the fuse block at the LS of the engine compt. So that "leg" wouldt be affected by a bad starter)
Turn the key, cranks slow, dome light dims/goes out, either the starter is drawing too much current, or more likely, the batt is low or has a dead/weak cell(s)
No, this all is not written in stone, but just a quick hint to help you narrow down what COULD be the culprit on a no-start/no-crank.