There are either three or four wires connected to the solenoid. The two larger wires are the high-current side of the solenoid and one of the two connects the battery to the solenoid and the other connects the solenoid to the starter. If the solenoid is a four wire the other two smaller wires are a ground wire and the other is power from the ignition switch. Use a test light connected to the NEGATIVE side of the battery and hold it on one of the small wire connections on the solenoid while holding the key in the start position - you may need an assistant to hold the key to override the seat safety switch. If the light does not glow try the other small wire on the solenoid and repeat the above procedure. If the light still does not glow you have a problem in the ignition control circuit and most likely one of the safety switches or the ignition switch is malfunctioning and not completing the circuit. It could also be the wires from the switch so check those, too. If however the light does glow on one of the small wires then check the other small wire to make sure it is grounded by connecting your test light to the POSITIVE side of the battery while touching that wire and the light should glow if the ground is good.
If you have a three wire solenoid the solenoid is grounded by the body of the solenoid and the only small wire is the ignition control circuit from the ignition switch. Can't say for sure what is bad until you do the above tests and report back with your findings.