Q: Once started, car turns off and backfires - 1996 Nissan 300ZX

Any time a car isn’t starting I remember the 3 things an engine needs to run. It needs air, fuel, and spark. It sounds like your starter is working fine otherwise you wouldn’t be almost running and backfiring. My gut says you aren’t getting enough spark. It sounds like at some point the engine may have been flooded. This happened to me recently on a turbo mazda engine. You need to check the spark plugs anyway, so pull your plugs and verify they look okay. While the plugs are out, use a bright flashlight to look down into the cylinder and look for a puddle on the piston top. If you see liquid in there, its probably gas and you should be able to smell it. If its flooded, let it dry out before reinstalling the plugs. Make sure the plugs are gapped properly. You can buy an inline spark plug checker that lights up if you are getting spark if you don’t know how to do it the "oldschool" way. Verify you are getting spark. If the plugs are good and you aren’t getting spark, then it might be the coil packs. If you have spark, then start looking into the fuel system.