Does the engine crank mormally? If it cranks too fast and unevenly, check to see if the timing belt has broken. If it cranks normally, check for spark. If no spark, very likely the distributor has failed. You need to check for power and ground before condemning a distributor.
If you have spark, then you need to check the fuel pressure. The pump should energize for a moment when you turn the key on, and should be running when the engine is cranking or running. The computer controls the fuel pump through the fuel pump relay. You can check for power at the pump with a meter or testlight.
If you need a Mazda specialist, here's a directory link for you:
PS: Please say whether your car is an automatic transmission or manual. The electrical systems are different.