Won't start Sometimes our car won't start. We can wiggle and push on fuses in fuse box under the hood and then it just decides to start up.

So it's a no crank condition? Do dash lights, gauges, and everything else work when the car won't crank over? If so, buy a cheap $5.00 testlight, and when the car won't crank, pull the small black wire off the starter solenoid. While someone holds the key in start (cranking) position and clutch pedal depressed, see if the black wire has power as it should. (Ground the testlight and just touch the wire's end terminal. If powered, the testlight will light up.) If power there, then the starter solenoid is failing. Toyota starters are very good units, but the solenoid's internal contacts get old and pitted.
If no power at the black wire, then the start circuit from ignition switch to clutch safety switch (on the clutch pedal) to starter relay to starter solenoid will have to be diagnosed. To double-check: take a single battery jumper cable and put it on the positive battery post connection. Put the other end of the jumper cable on the solenoid terminal where black wire was removed. Key can be off. Make sure car is in neutral, brake set. If starter now operates, solenoid is O.K., and it is a problem in the start circuit, -ignition switch, neutral start switch, or in the wiring.
Now find a grounding place for testlight under the dash. When car won't crank, check for power coming out of ignition switch on the black wire with white stripe. This is the start wire for the starter solenoid. Key must be in crank position. Wire shoud be powered-ignition switch is working. If no power, switch is failing. You can do the same for the clutch start switch-it's a simple switch, that when clutch is depressed switch is closed and passes power on from ignition switch to the starter relay (thus allowing power to the starter solenoid). Black wire, red stripe-this is wire from clutch switch to starter relay. When key is in crank, clutch depressed, this wire should be hot.
With me so far? Still haven't found a problem, or any loose connections? Next and last is the starter relay. It is located under dash, close to gas pedal, but under the center console, just forward and left of gear shifter. It can be tested and the wiring diagnosed there, but relays are cheap, so just swap in another and see if that helps.
If you have tried everything, and still no help, you could try a new wire from the relay to the starter solenoid. This is that black wire we started with. Older toyotas sometimes have a problem with degraded wiring not passing enough current to operate the starter