If it has spark, gas is making it to the cylinders, and the cylinders have compression, and it's in good timing it should make at least some indication that it wants to start. I might be wrong, but I think the CPS just let's the computer know what the RPMs are (I think I'll start my car and unplug it to see if it stalls, obviously I couldn't drive it, but it might start or run?). Anyway, I would be surprised if the CPS had anything to do with it.
But a weak spark might be a problem.

The plug wires on these engines should really only be removed with plug wire pliers. Obviously it can be done without them, but they are on pretty tight and deeply seated, with time and heat they can be clamped in there real tight. If you grab them at the wrong place and pull them it's very easy to pull the wire out of its metal connector as it comes off. In many cases the wire will still work by arcing to its connector inside the boot, [perhaps] creating a very weak spark.
Likewise, even if you don't yank any wires out of place, the boots need to be pushed ALL the way in until they are tightly gripped on the plug and all the way forward. It should feel pretty firm laterally as well, that is, they should feel relatively stiff when wiggled side to side. Once again, failure to do this could mean that the wire connector may not be in contact (or tight contact) with the plug terminal and [perhaps] causing a weak spark as above.
A combination of the two is certainly worse yet.
I say "perhaps" in brackets because an arcing spark can sometimes (if it's not arcing too far) actually intensify the juice to the plug. In the 50-60s they used to sell "spark intensifiers" that went on the ends of the plugs ahead of the wires and were basically just a measured gap for the spark to arc across. Some kits had transparent tubes so you could watch your poppin' engine give a light show. I once had a mopar with a fouling plug and temporarily pulled the boot away from the plug so the arcing spark would make the plug fire hot enough to keep it from fouling until I had the time to fix it.
Actually, with that in mind, it might help to have someone crank it at night and see (and listen) if there are any wires arcing.
Make sure the coil wire is secure on the coil, look for grey/black chalky marks on the coil wire where it comes close to/touches metal engine parts. Also, if you did the job on a rainy, damp day maybe the dist. cap got damp or is arcing out along a trace or a crack. Lastly, if the dist. cap is 20 years old the carbon center contact might be fouled or just about worn out.

All weak suggestions I know but might possibly help.