My bet is electrical portion of ign switch (easy to fix) or dirty battery terminals (even easier to fix). If the solenoid is bad, you will usually get a click as the core extends, but arcing corrosion keeps it from taking juice to the starter motor. There are a ton of connections between batt and solenoid, any one of which could be intermittent. The most usual are the ign switch and the solenoid wire terminal, which can get some corrosion from living outside.

To test my hypothesis, jumper from batt terminal at starter to solenoid terminal. Engine should crank, but won't start unless ign is on in run.