1--It is possible that you slipped the timing chain. A couple of quick checks are (refer to factory shop manual)
The closest manual (don't use the wiring diagrams for your '73) is this 72 manual thanks to AbodyJoe:
[ame="http://www.abodyjoe.com/pictures/Misc.%20car%20info/1972%20Plymouth%20Chassis%20Serv%20Man.pdf"]http://www.abodyjoe.com/pictures/Misc.%20car%20info/1972%20Plymouth%20Chassis%20Serv%20Man.pdf[/ame]
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A---estimate the cam timing by the shop manual method above
B--use a timing light while cranking with THE STARTER to see where timing is and whether it moved, assuming you have not changed it
C--You can also get some idea of timing chain condition by using a socket on the crank, watching the rotor, and see how far the crank moves back--forth without moving the rotor. This will give you an idea of chain slop
2--Even though you think you have spark, there may be some problem that is causing a WEAK spark. I like to check spark right at the coil tower with a grounded clip lead and probe / screwdriver. You need to crank the engine USING THE KEY as this changes the electrical setup. In a pinch, you can run a jumper to the coil + terminal You should get at least 3/8 and typically 1/2" nice blue hot spark
3--As stated above, it might be that the needle / seat are stuck or plugged with dirt, and the carb continues to flood. This can be determined by looking down the throat of the carb without pumping the throttle and cranking the engine. If you see a stream of fuel either out of a vent or the venturi boosters, you'sa got problems.
4--Is it possible that you have CONTAMINATED fuel? Maybe some "friend" put something in the tank, AKA water?
There is THREE basic things an engine needs to run
1--Compression, so run a compression test
2--Spark -- a good hot one, and at the right time
3--Fuel -- not too much, not too little, but frankly on a "clean fire" with good spark and plugs, I've test fired and ran engines for several seconds by squirting fuel right down either an open manifold or a carb with no fuel to the carb
Yep. Hooked a battery, my "emergency test ignition" to this and threw some gas down the carb, and you would be absolutely correct, there are no exhaust manifolds!!!
This is my emergency / test ignition.
Inside here is an HEI module, the coil. You hook up ground and battery, (breakerless) distributor and coil, and you have fire