I am not aware of another relay in addition to the ASD. You don't always get a code with a bad Hall sensor. Also, potentially bad connection to distributor. I think on the Turbos you need two signals from the distributor (maybe Hall sensor signal and a sync signal?).
I think if the ASD is good you will initially get some fuel, but if there is another problem (such as with the distributor or a connection), the ASD will cut off fuel supply after an initial start attempt.
See this link for some tips on troubleshooting the no start - no engine feed section.
http://www.minimopar.net/electrical-powerfeeds.htmlHere is something else you can check on the distributor (plastic disc loose - see link)
http://www.thedodgegarage.com/turbo_ignition.htmlAlso, if you have low voltage due to a low battery or from a voltage drop (bad (high resistance) power feed line or ground line), and the voltage at the computer is too low when trying to start the computer might not function properly or the injectors may not be turned on and it might not start. For starters check you battery terminal connections.
Since you are only getting the recently disconnected battery code, it may imply that your voltage at the computer is being dropped too low during the start attempt when you crank it and you are not storing codes and you are resetting the computer each time you try to start it. (The voltage will always drop off somewhat during start because of the high starter current draw - but if it goes to low you can have problems.)