It is hard to say what the problem is.
Here are some guesses.
I have not heard of anyone running a 343 pump yet. I would bet that it draws at least 16A current. Most people are rebuilding with pumps that draw 12A or even 9A. See the fuel pump Guide in the "How-To Tech articles" that I pointed to in the last post. The magneto only puts out about 18A, so if you use most of the power running a pump, the MPEM gets "starved" and acts up in a number of ways.
I assume you are talking about the fuses on the MPEM up front, not fuses in the electrical box in back. If so the most forward 15A is for the injectors, while the 15A at the back end is for the fuel pump. It obviously won't start without either. If you mean it won't crank (ie. won't even turn over) possibly the MPEM is not allowing starter solenoid actuation. I don't know what you mean about all the resistances off connector #4 checking out OK, since there are a bunch of unrelated components.
If the fuel module plug individual wire connectors are not staying put, the metal connector "prongs" are damaged or not bent the right way. The wires should stay (click) in the connector and not need glue. Also once the connector is plugged in, if they don't stay firmly attached to their counterpart then they are damaged, and should be repaired or replaced, not glued.