1995 3.4L Camaro

Do the gauges and warning lights work with key on? If not, check fusible links, AM1 for ignition key power. If the gauges/warning lights work, the key switch has power, so you can follow it to the starter solenoid. The start wire out of the ignition switch is a black/white wire, this is the hot wire to the solenoid, and only has power when key is held in start. With automatics, there is only one switch-a neutral start switch- between the ignition switch and the solenoid on the starter .

With a manual transmission, the black-white start wire goes to both a starter relay and a clutch start switch (on the clutch pedal), those two work together to send the power on to the starter solenoid. So, no crank, good battery, power to key, follow the black/white wire, the start relay and the clutch switch, to the starter solenoid- a hot wire there turns the starter motor on.

There is no starter relay shown in a wiring diagram. The only thing between the ignition switch and the starter solenoid is the park/neutral switch (or the clutch pedal position switch on manuals).

Do the warning lights and gauges come on with key on? That would verify power is into the switch and being sent out. The small purple wire on the starter solenoid should have power on it when the key is held in start position. If it does, recheck your starter and battery connections. When the purple wire energizes the solenoid, the starter motor should crank the engine.
If no power on the purple wire in start, check the neutral safety switch or the clutch switch if a manual. The start wire out of the ignition switch is a yellow wire, and the wire from either safety switch to the starter solenoid is a purple wire.
(The power to the ignition switch is from the 50 amp Ignition fuse in the under hood fuse block.) See? The positive battery cable is connected to the starter, but not to the starter motor. When the key is in start, the hot purple wire energizes the solenoid and the battery cable is connected to the starter motor.

You could check for power on the small orange wire at the starter solenoid on the starter motor-with the key held in start position. Should have power there in start. If you do, take starter off to be tested. If no power, signal is lost between ignition switch and the solenoid. Next find the starter relay under the hood. Hold your finger lightly on it while someone turns the key to start. If you feel a click or movement, check orange wire from there to starter solenoid. If nothing at the relay, move to the starter clutch pedal position switch- a simple on/off switch-check for power to the switch with key held in start. With clutch pedal pressed, it should pass power on to the starter relay, with key in start. If you have no power at the clutch switch in start, between there and the ignition switch is the Burglar Alarm Relay and the BCM box. The start wire out of the ignition switch goes to the alarm relay, and another wire from relay goes to BCM (body control module) to activate the relay so power will pass from ignition switch to clutch switch. That's all, Nathan, pretty simple but then again, not...better invest in a test light or digital volt ohm meter (DVOM). Good for checking electrical circuits, hope its not the alarm or BCM.

Where is this relay? A wiring diagram doesn't show any relay at all in the starting circuit. Just this: a yellow start wire out of ignition switch goes to the neutral safety switch (if manual, a clutch start switch on the clutch pedal: if automatic a transmission range switch); From the safety switch a purple wire to the starter solenoid on the starter motor. Only other place to check is a "crank" fuse in the instrument panel fuse block- a 10 amp fuse in position 8 of the block.
Is the click you hear possibly from the starter solenoid? If it is, that means key switch part of circuit to the solenoid is good. Either starter motor is bad, or battery connections to starter and to battery ground may be bad, check them first.

Can you push it off and pop the clutch in 2nd gear to start.

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

Your diagram is below. Since the starter jumps at the solenoid, the problem would be the ignition switch, the clutch interlock, or the wiring. Check for power at the yellow wire that goes to the switch under the clutch pedal when the key is turned to start. If you have power on the red wires to the ignition switch but no power coming out when the key is turned to start, replace the switch. If you DO have power on the yellow wire, try bypassing the interlock by pulling the connector off and connecting the terminals inside the connector with a large paperclip. If that doesn't work, the purple wire from the interlock to the starter solenoid may be broken. Please let me know if you have more questions.

there should be 2 wires (plus a connection to ground, which I think is made by it being mounted to the engine), the Purple one goes to the ignition switch (I think this should be the Yellow wire at the ignition switch side), the Red goes directly to the battery at the starter solenoid
ie...
Red from battery (fused) > ignition switch (yellow wire) > Park/Neutral position switch or clutch pedal position switch [pending which transmission you have] (changes to purple) > starter solenoid

I'm adding an image, but I don't know how readable it will be.

When you turn the ignition key to start your car, voltage from the battery flows through the ignition switch to the Park/Neutral safety switch and/or brake pedal or clutch pedal safety switch (you have to push the pedal down before the circuit will complete) to the starter relay or solenoid. When the relay or solenoid is energized by voltage from the ignition switch circuit, it closes a contact that routes more power from the battery directly to the starter to crank the engine. The starter motor spins, pushes the starter drive gear to engage the flywheel and cranks the engine.

Low battery (Check battery voltage, recharge if low, or jump start with another vehicle or battery charger).
Loose or corroded battery cables (Inspect, clean and tighten BOTH ends of BOTH battery cables).
Bad starter relay wiring connections or ground connection (Inspect, clean, tighten wiring connections).
Bad starter relay/solenoid (Check for voltage at relay, if relay has voltage but there is no "click" when key is turned to start, replace relay).
Bad starter (Jump battery voltage direct to starter to see if it spins, or remove starter and have it bench tested at auto parts store).
Damaged starter drive or teeth on flywheel (Remove starter and inspect drive gear and flywheel teeth, replace damaged parts if necessary).
Bad ignition switch (Check to see if voltage reaches starter relay/solenoid when turn to start. If not, check for open P/N switch and brake or clutch pedal switch. Replace ignition switch if defective).
Open P/N safety switch, or open Brake Pedal Safety Switch (automatic transmission) or open Clutch Pedal Switch (manual transmission). Bypass switch with jumper wire to see if engine cranks, or use test light or voltmeter to check for voltage passing through switch when ignition is turned to start.
Engine seized due to bearing failure or internal damage (Use socket and long handle to see if engine can be turned by hand, if not engine is locked up).
Engine hydrolocked due to coolant leak from leaky head gasket (Use socket and wrench to see if engine rotates, remove spark plugs and see if coolant comes out or engine can not be cranked with plugs out).

check to make sure the clutch pedal switch is functioning and that the floor mat isn't blocking the clutch pedal from hitting the switch, basically its either the clutch pedal switch or something between the ignition switch to the starter but i'd try the clutch pedal switch first, its the easiest to check