Sometimes it starts...sometimes it doesn't

Within the past couple of weeks, my 1991 Toyota Corolla randomly decides it would rather not start. (Sometimes it starts just like usual.) When I depress the clutch and turn the key I hear a click, and if I keep the key turned for a second or so, I can make out a slight hum as well. I can compare this to when the clutch is not depressed and turning the key has absolutely no effect, so I know that something wants to happen. The battery also has power, as the car will start after a number of attempts (sometimes 1, sometimes 20+). The battery is nearly at the end of its rated life, but I don’t understand how it can be the problem since the car will eventually start. Any suggestions on what may be the problem, or ways I can attempt to diagnose this problem?

Sounds like your starter solenoid isn’t kicking in, possibly a combination of wear and low battery voltage. One way to verify this is to have an assistant turn the key while you take a metal rod (jack handle works well for this) and hit/tap the side of the solenoid (don’t be a moron and leave the car in gear or you’ll get run over if it starts). If that’s the problem, before replacing the solenoid, check your battery condition, the condition of the terminals, the battery ground, and the connection to the solenoid from the battery. Another possible problem spot is the ignition switch.

pbanders is right. The contacts in the starter solenoid switch are probably worn out and just barely making contact on a good start. The ‘click’ is when the contacts don’t make and the starter just sits there with the pinion gear engaged with the flywheel ring gear but the motor is not turning because the heavy power has not been connected.

Thank you all so much! Your responses confirm the hunch of a passerby who witnessed my attempts to coax the car into action. I am a student and finals are next week, so I won’t be able to replace the solenoid before then. I’ll make sure to keep a good solenoid-whackin’ bar with me! Thank you again for your help.