The NSS only affects cranking of the motor and backup lights. If the motor is spinning, then the NSS is doing it's job. Try this: Don't turn the key quite as far into start. Just till it barely cranks and see if it catches. The solenoid has an ignition pickup on it (contact marked "I") and you should check first to see if the wire to it has power with the key on. (it should be about 8-10 volts) If it does, then the wiring should be okay. The solenoid contact should come to life while cranking. You can check with just a test light. If you have a voltmeter (I have a digital cheapie from Harbor Freight) you can check the power from the battery when cranking. Less than 10 volts means the battery is too weak for the coil to make strong spark.
I changed my ignition coil out (if you don't have a GM HEI dist or the TFI upgrade) for a Napa IC12 or the cheaper IC12SB which has better coil output voltage and got rid of the horseshoe connector which is a corrosion magnet and spark killer. (just make sure you have it the right way around or the sparkplugs will fire backwards, causing poor spark)
If you still have a no-start issue, then test for spark. Bad plugwires or especially a bad coil wire can cause no-start. Crud on the coil "cone" can cause arcing, killing spark. Same with the dist cap. Corrosion inside coupled with material stuck to the outside or inside can cause arcing. I do NOT like aluminum contact caps because they don't last 1/2 as long as brass ones. The ignition rotor can also arc or track, drawing spark away.
If the choke doesn't close almost all the way, then fuel may not be drawn in and the lean condition won't start (flooding from a too tightly closed choke can do it too) I pump the gas 3 times when it's cold out and without my foot on the gas, it fires right up. More or less pumping means no start. If the fuel filter with 3 lines is used, you have to make sure the bypass line is in the top position or gas will drain back overnight.
That should get you started (barring other issues)