I am not getting a signal to fire my solenoid on my starter. I am not sure if it is the ignition switch, neutral safety switch, or something else. I don't even know where they are. Is there a common problem associated with this?

Check the starter solenoid and the connections from the battery to ground, battery to fusebox, ignition key switch, neutral or park safety starting switch, solenoid, and solenoid to starter. Make sure you have ignition key switch wires connected to the solenoid - without them - the solenoid can not close to send 12V to the starter.

I think the purple wire (or maybe the yellow) from the neutral safety switch goes to the coil side of the starter relay, turning it on so power is sent from there to the starter solenoid. You could check for this signal to the relay with a test light. The key must be held in start while you probe the other two terminals for the relay. If the signal is there, either a bad relay or the coil side of relay is not grounded properly. It is possible that the coil side ground is the neutral safety switch-grounding the relay's coil side only in park or neutral-in which case the nagging light on shifter (between off and run, it only works?) may be telling you the safety switch is the problem.

You may need to look at a wiring diagram, Greg. But the starter relay is the last component in the start circuit before the starter solenoid. From battery to ignition switch to "crank" fuse to neutral safety switch to starter relay to starter solenoid to starter-and back to battery through ground. That is the start circuit. Just that the wiring tying them all together makes it complicated.

No, the starter is grounded to the engine block, . The neutral safety switch, Or gear select switch, is the midpoint for the 12v crank signal from ignition switch to the starter solenoid.

you have the solenoid on the fender, and this is the wire coming from the neutral safety switch ?

Is power getting to the ignition switch? Do the warning lights and gauges come on when key is turned to on? That would verify power in and power out at the switch. Then you would need to check the start circuit. A single start wire comes out of the switch, the signal travels through the neutral safety switch and a starter relay and then to the starter solenoid mounted on the starter. Solenoid closes contacts so battery power can operate the starter. If new starter doesn't work, power has been lost between the ignition switch and the starter.
If no power to the ignition switch check maxi fuses, all fuses in fact, and possibly a fusible link from the battery that may be the feed for the switch.

Something wrong in the start circuit. The fact that dash lights come on indicates the ignition switch seems ok.- power is getting to it and exiting it.

The next place to check is the starter: before taking it off and have tested, do this quick test: when the car won't crank over, pull off the small wire on the starter solenoid-mounted on the starter-and see if that wire has power when the key is held in cranking position. You will need a helper to hold key in start, and an inexpensive testlight or volt meter to see if the wire has power.
This wire is the signal wire from the ignition switch to activate the solenoid and allow battery power to turn the starter motor on.
If the wire has power and still no crank, then the starter or solenoid is the problem, assuming battery and cables are good and connected tight. Pull the starter off and test it. If starter is good, probably the solenoid.
If the wire has no power when key is held in crank, the problem is in the circuit from the ignition switch to the solenoid-includes the neutral safety switch, maybe a starter relay, too. One would begin testing by checking for power on the start wire exiting the switch with key in cranking pos. If good there, test the neutral safety switcfh. If you have manual transm, the switch would be on the clutch pedal. If automatic, have a shop locate and test that.
Good luck- often, not always, it is the starter or solenoid. But do that check for power at solenoid , first.

If the problem is the starter won't crank the engine over, check the small wire at the solenoid (the one from the ignition switch). It should have power when the key is held in crank. If no power there, trace the signal back to the ignition switch-check the neutral safety switch-at the clutch pedal-or the park/neutral switch on the transmission, if automatic. Check if the ignition switch has power out of it on the start wire with key in crank. Use a voltmeter or testlight for checking.

I don't think so. I got a 95 and I've done all kinds of electrical checking for various things and to my knowledge there isn't. There's fuses for the ignition and engine along with other electrical items but no specific computer fuse that would turn off a computer. I assume the car won't start?

If your car is simply not starting it could be something as simple as the neutral safety switch if you only hear a click turning the key. Disconnect under left side dash. White and has a green and black wire coming from button behind clutch pedal.

If car cranks but just wont start then could be numerous things. Check the 30 and 40 amp fuses under hood. Make sure battery terminals are connected tight and clean with brush tool if needed. If battery is fine and charged, I assume you have checked, then I'd focus on the ignition system.

ignition switch (in steering column)
neutral safety switch (disconnect above pedal)
starter relay (under radio)
starter solenoid
starter

If cranks then neutral, ignition and relay switches are fine
If clicks then ignition and relay fine but neutral switch or solenoid may be bad

Use a test light and check at the starter solenoid and see if the ignition start wire gets hot when the key is turned to start. If it does check to see if current then goes thru the solenoid to the starter. If it does check to see if current gets to the starter, if it gets to the starter the starter is bad. If no current to the starter or out of solenoid the solenoid is bad. If current does not get to the solenoid when switch is turned, check and see if the current goes thru the neutral safety switch (Clutch switch if not automatic). If the current doesn't go thru the switch replace the switch. If you are not getting current to the switch in the first place check the ignition switch. If the current doesn't come from the ignition switch to the safety switch replace the ignition switch.

He's right I would check Neutral safety switch first. Make sure B+ only comes out of one end of it when pedal is released. Only time B+ must be out of both sides of this is when pedal is depressed. Ignition switch can't go to starter directly B+ starts at ign switch to neutral safety to solenoid on starter.
Most neutral safety switches can be adjusted.