Hello.
Try this: Without touching the gas pedal at all, turn the key on for a few seconds, then off, then on for a few seconds, then off again, then on again, and then crank it without touching the gas. If it starts, the problem is fuel pressure related. Rent a fuel pressure test gauge from the local auto parts shop and see what readings you get. While I know you've replaced the pump already, it wouldn't be the first, or second, or third time I've heard of a defective aftermarket fuel pump. They're pretty common, unfortunately. I'm attaching Prodemand's instructions on running the fuel pressure test in the images below. Also, we have a more general guide on that here:
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator
Has the timing belt ever been replaced? The car is 26 years old and according to Mazda it should've been due at about 60,000 miles. If that hasn't been done, do it now, before the timing jumps on you.
I'm attaching images containing Prodemand's instructions on how to do the job specific to this car. And here's some general information on timing belts:
https://www.2carpros.com/articles/how-a-timing-belt-works
Start with checking into these things and we'll go from there.
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Tuesday, October 5th, 2021 AT 8:10 PM