When you say "The cap is a NEW NOS cap! Spark plug wires are NEW NOS! Of course it has spark"... have you actually verified a clear strong blue spark when cranking, or are you just assuming it should have spark because those parts are new and installed?
VERIFY
An engine needs three things to run:
Fuel, air, & properly timed spark.
As noted before by other posters, verify those things 100%. The trouble shoot what's missing.
1) No fuel? Start at the fuel pump and work towards the carb to see if fuel is getting to the combustion chamber.
VERIFY
2) No air? Hard to not have air... but...
VERIFY
3) No spark? Start at the spark plug (grounded to engine to see spark), and work towards diz and coil. Coil won't operate without key on 12V... Coil 12V can be shorting out against engine due to old wiring insulation. Coil won't fire if diz does not send appropriate signal... Diz won't send signal to coil if rotor/points/other parts aren't set to spec. (This is old style points ignition talk - same applies with an electronic ignition system, but the module must be a known working unit, properly hooked up. Don't assume, VERIFY).
Once you verify all 3 things above and the variables they can have, then timing is the next key step... you must verify TDC at #1 cylinder, and time ignition accordingly.
Good luck.