Are there any other electrical accessories that don't work? Specifically, does the heater fan work?
There is a possibility that one of the fusible links coming off the battery has failed (actually, has done its job) and is no longer completing the circuit of the starting system. I had to repair precisely this problem last year on my brother's van.
Once you get this problem sorted, it is a very good idea to switch form the computer controlled ignition and carb to non-computerized ignition and carb.
Here are the 84 Dodge van wiring diagrams- an 84 Dodge truck should be virtually identical:
However, none of this will solve the problem with the battery not holding a charge. Batteries not holding charges are due either to (a) a short somewhere and/or (b) a fault in the battery.
To help find the short, pull the (-) battery cable. Connect a test light between the (-) terminal on the battery and the terminal on the (-) battery cable. If you have a short, the test light should light. Leave the test light hooked up and begin pulling fuses one by note. Note after which fuse is pull the light goes out. When the light goes out, the fuse you just pulled powers the circuit with the short. Use the wiring diagram above to trace where the short might be on that circuit.
If you pull all of the fuses and the test light never goes out, check for correct installation of aftermarket accessories such as amplifiers, stereos, lights, etc.... You also should check for frayed wires or melted insulation in the wiring harness. Good luck.