Whats blowing up in my engine?

[NM5K]

No. Not unless it does not turn at the normal speed
with a fully charged battery. Have you checked the plugs?
I wouldn't be half surprised if they were not gas fouled
after all this. Backfiring usually indicates a timing problem,
but I imagine there are a few cases when the carb could
cause a backfire.
But I'd make sure the plugs are dry before I did anything more.
And also.. They can look dry to the eye but still be fouled enough
not to start. I've seen it a few times on older plugs that were semi
encrusted with deposits, carbon, etc.
If they are brand new with no deposits, but are wet, you can
usually dry them out real good, and they will work.
And yep, the easiest way to make sure you have #1 TDC is
to pull the #1 plug, and make sure the cylinder is fully up
towards the plug hole. I'd unplug the coil before doing that
so it won't try to start. You can take a short dowel or rod to
measure how far the cyl is from the hole. If you are 180 degrees
off, the #1 cyl won't be in the up position.
When you have that set, with the timing mark at TDC,
the rotor should be pointing towards the #1 plug wire tower on the cap.
I wouldn't buy any more parts until you actually prove they are bad.
You have to diagnose the problem.
If you have never pulled the distributor, it's probably still right,
and I would not mess with it if the rotor points right.
Only if I suspected say maybe a sheared gear pin would I yank
the distributor at this point.
Being as it ran fine before the new battery, I think the non start
problem was something really minor like fouled plugs, or problems
getting fuel to the carb.
My 74 F-100 gets fuel flow sluggish cuz it sits all the time lately.
I sometimes have to prime the carb with a shot of gas a few times
to get it's juices flowing again, and not overheat the starter trying
to get it going by just cranking.

[wildcard]

Not likely if it's still turning the engine over.