you need to find out if the distributor is sending the signal to the computer and/or if the computer is sending the signal to the coil. There are two wires at the coil. One power in run and start. the other is ground from the computer. If you coil is marked, take the (-) ground side off. turn the key on and see if the coil has voltage to the (+) side. If have enough voltage to light up a test light that should be ok. If not, check fuses and power from ignition switch. If power to the coil is good check the wire from the computer to the (-) side of the coil that you took off the coil. it should have a blinking ground while cranking. It probably won't because if it did your coil would have spark.
The distributor has the pick up coil and an ignition control module. Pick up coil makes an AC voltage signal. the module converts the ac signal into on/off signal for the ground for the coil. you will need a waveform viewer to check the signal from the distributor. If you have a graphing multimeter you can hook it up to ignition coil
(-) and ground. here's the problem. they only give me specs for 800rpm and 2500rpm. 800rpm should be 27 Hz frequency. 2500rpm should be around 83 Hz. They don't five a spec for cranking, 150 to 300rpm. But it should be something less than 27Hz but I don't know how much less.
distributors going out is common. pick up coil or module... But the computer for this era mazda is known for failure. it has a mitsu. computer and they are known for having a capacitor going out and turning off the computer. there is a place that can repair this computer. http://www.ecmtogo.com
they have a phone # you can call and talk to them about the problem if the distributor is not the problem. ALWAYS CHECK YOUR POWER AND GROUNDS FIRST THOUGH.