1...First you need to really really REALLY resolve the cranking issue, which may NOT be an issue
1A...Why are you using a remote switch?
2B..I need to get clear in my mind.........if you hook up the switch and it will not crank, and you then try the key, does it crank? If so, this is a poor quality or defective starter switch, one which cannot handle the current
3...Try your "remote" without USING the remote. Simple. Any metal object, a screwdriver, a quarter, or pair of pliers. Jumper across the two large bare terminals on the starter relay. Be careful of course, that it's in neutral, park. If it will not crank under THAT condition, you are right down to the starter, the cables, or the battery.
"New" does not mean functional
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4....If the cranking "issue" turns out to be the starter switch, using one to check spark IS NOT PROPER in that it does not give you the correct "picture." This is because, during cranking USING THE KEY, the ignition switch bypasses the resistor, giving you a hot spark
4B....Therefore, for spark check under "normal" cranking conditions, "rig" a test gap right in the top of the coil (in other words do not use the factory coil wire) and "rig" it so you can see it, say, through the hood gap. Then twist the key, and observe the spark that way. You should have at least 3/8" and typically 1/2" long hot blue spark (Easier to see with a small block LOL)
5....I would not waste time, get the starter "issue" solved, check the spark under proper conditions. THIS IS MORE LIKELY a fuel boil / vapor lock issue.
On my Dart, before I "went" EFI, the best things I did was to build a 440-426 style fuel return setup---using a Wix 33040 /41 filter with a built in return
Used a thick isolator gasket under the carb
And a rear mount electric pump.