Before we talk about reassembly there are two points I'd like to clear up.

First, when you initially took the carburetor off the petrol tank, was there any petrol in the well under the main jet, where all the brown crud was collected? The function of the fuel pump is to continually pump fuel into that well, allowing it to overflow from that compartment and return to the main fuel tank. If that well was dry, the fuel pump was not working at all. If it had at least a centimeter of fuel in it, the fuel pump was working well enough for the engine to start and run, unless the main jet was blocked. Hence the answer to my question can tell us the cause of the engine not running in the first place.

Second, could you please look closely at the diaphragm, checking for thin spots or actual cracks or perforations, especially where the piston/cup bears against it. If it shows signs of deterioration it would be appropriate to replace it while the carburetor is apart.

Once those points are cleared up, it will be time to clean that rather claggy petrol out of the tank, and reassemble the carburetor. Here are the assembly instructions for the fuel pump:
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Note that the diagram shows a carburetor with two plastic pickup tubes, which applies to a different version of the Pulsa-Jet that has a main jet mixture adjustment. Your version, with the second pickup tube incorporated in the metal carburetor body, has only an idle mixture adjustment. The actual assembly instructions apply equally to your carburetor.

Please refer also to the disassembly instructions when you are putting the fuel pump together. Carefully engage the dowel/roll pin on the body with the hole in the cover, and ensure the cover pulls down evenly as you do up the cover screws.

When you come to putting the carburetor back on the tank, and connecting the links, levers and governor spring, the process is just the reverse of disassembly. If you are unsure, please stop and say so - we'll work it out from first principles.