If the starter solinoid doesn't pick when you put the key in the start position, then you probably have an open circuit or a blown fusable link. You can check the lead on the small post for 12V with a volt meter. Put a meter on that post and have someone turn the key to the start position. If no voltage, it is most likely the neurtal safety switch or connection to the switch located on the transmission by the shift linkage. Connections in this area are prone to corrosion. Try resetting the connection and use dialectric grease or bulb grease to seal the connector.
The path is normally Fusable link to ignition switch, to jumper under left side of dash near where a clutch would be if you had one. If you do have a clutch they use a switch mounted on the peddle instead of a neutral safety switch and there is a jumper bypassing the neutral safety switch position. If no clutch there is a jumper and then the dircuit goes to the neutral safety switch and then to the starter solinoid.
If the 12V side OK, check the ground side. As far as grounds go, starter solinoids usually are grouded by the mounting screws. You may also have a bad ground to the engine block or/and to the body.
All this can be done witha common multimeter using either the voltage scale, ohms scale or continuity function.
Good luck,
>-