The fuel computer gets a speed signal from the ignition computer that tells it if the engine is turning over, then it engages the fuel pump relay which turns on the fuel pump. So if you have no primary ignition trigger, you will have no fuel pump by design.
The sensor attached to the no. 1 plug wire is the equivalent of the cam position sensor in the later cars - with the flywheel sensor only, the computers have no way of knowing whether a cylinder is on the power or intake stroke.
Sound like you should change the cap, rotor and wires, which may solve your problem. If not, look for ignition primary - pulsing at the negative side of the coil. Other common failure points are the flywheel sensor and the power stage. The power stage is the device that switches the high primary current to the coil and is mounted on an aluminum heat sink on the inner fender near the air filter box.