The first step to getting a good answer is to ask a good question. How do you make food? That is not a great question. At what temperature and for how long should I bake a two layer birthday cake? That is a much better question (if you want an answer). So back to your question, here's an example of how your question might have have been better written: My 96 Miata cranks but will not start. The "check engine" light comes on with the key, and everything sounds normal but the engine simply won't start. The car has 125k miles but has not had any major service in the last 3 years. The car was running perfectly until I tried to start it this morning. The car does seem to be cranking rather fast. Anyone have any ideas? [broken t-belt!] So ask a better question and you might get some good answers... or get it towed to a good shop.
Belt slipping? Bad bearing in belt driven accessory?
The oil change usually helps quiet the lifter noise. You could replace all 16 hydraulic lifters if it really bothers you. Most Miata owners just live with it. Try 10W/30 oil.
probably cam positionong sensor.
Does it turn over? Does it have fuel, spark and compression?
Where is location transmission plug on Mazda 96 626
chances are to start with the fuel filter if that's not it try the fuel pump
Check for fuel Check for spark
Check for spark Check for fuel
Type your answer here... It could possibly be the ignition switch.
Try adding more gas...
What make and model ford 6 cyc will fit 96 mazda
Check the timing belt.