2001 rodeo won't start. the solenoid on the

The clicking is the start relay which u don't hear unless the starter doesn't work, u have a defective starter solenoid, the internal contacts are burned, this is a NipponDenso style starter and they all have this same problem, u can replace the starter, replace the starter solenoid or replace the copper contacts in side the solenoid for around $12.00 USD

Unfortunately if the soleniod is on the starter, and it is clicking, then the circuilts to the starter are probably fine, and it leaves the starter itself as the main suspect.
One thing you can do is to turn the engine over a little by hand, under the hope that maybe the starter bendix gear is jamming on the flywheel. With different positioning it may unjamb.
The next would be to check battery voltage. If you have a meter, it should be about 12.5 volts before starting, and about 10 during. It is does not drop then it is the soleniod itself. It if drops below 9 volts, it is likely the battery. If you don't have a meter, you can just turn on the lights to get some idea, because the lights should dim while trying to start, but not go out completely.
If you decide it is the soleniod and want to try fixing it yourself, it is not hard to take the starter off and remove the soleniod. Bascially the solenoid is a large electro-magnet, that thows a steel rod, pushing the main starter contact switch, and throwing out the starter gear. The contacts can be burnt or oily and need cleaning. Or the shaft can be adjustale, reaching gear limts before making switch contact. The solenoid shaft usually has loop on its end, that goes over a lever that throws the gear out.