if it has fuel or stater fluid and it has spark then most likely ecm timing issue, coils most of the time only fail when warm and then work when cool. it could be low spark voltage. did you check your fault codes? try starting with jumper cables?
When you first turn on the key and the run switch, do you hear the fuel pump come up to pressure? It should run for 4-5 seconds before it hits full pressure. If you can't hear it run then the fuel pressure is not high enough to fire the injectors. My FLHTCUI had a heat sensor between the heads go bad. It tell the ECM its too hot and the fuel pump won't run. It sounds like it will run on starting fluid--it has to be fuel related. Put your head down by the tank and hit the run switch, you should hear the fuel pump.
there should be a quick disconnect on the injector hose just behind the horn. be careful not to break it as it cost $50. after you remove the connection and turn on the key it should pump like crazy. if it does then your down to the ecm or a sensor. you have 2 fuel injectors so i dont think both would go out. let us know what you find
it could be a sensor telling it to cut off the injectors. ecm are not cheap but you should be able to find a used one from motor cycle salvage. you going to want to check for a pulse on the injector first. may require some test equipment like oscilloscope.