I fail to see the connection to the fuel pumps if the battery is dead and the alternator has insufficient output to keep the spark going.

Your problem appears to be a failure to charge the battery.

My guess is that it will start just fine with the recharged battery, only to repeat the same problem if there is no alternator output.

I'm not really concerned with the starting voltage now that the battery is recharged. If the engine does start, check the battery voltage while it's running. My guess is that you'll find 12V or so.