If you have a good old fashioned auto electrician in your town I would suggest talking to him. Given the car is fairly old the stater motor may need new brushes and it is always possible it will need a complete re-build. He should also be able to identify and replace the starter relay. The starter motor will have a brand and model ID stamped on it and the relay will probably be the same brand.
A solenoid is a combination relay and a device that moves a sliding iron core with the creation of a magnetic field to throw the starter gear out. It would always live on top of the starter motor itself and looks like a cylinder that rides piggyback on top of the starter motor. Some starter motors use a different system which throws the gear out when the starter motor starts to spin. They would have a separate relay. In some cases even a starter motor with a solenoid may have a separate relay to protect the starter button or key switch from high current loads.
In either case the older systems can generally be repaired or replaced without huge expense and a competent auto electricians workshop should be able to do the work fairly quickly.