My car turns over good, acts like it might turn on then continues to turn. I figure it might be fuel filter since low fuel light had come on.Or could it be th fuel pump got hot and is not working properly?

Bad ground tank to chaise

Common problem is turning car off with engine not reaching normal operating temp and floods engine. try this. DE-CHOKING PROCEDURE WHEN ENGINE CRANKS BUT DOES NOT START
If the engine does not start, try the following procedure to start the engine using the de-choke mode.
Failure to do so may aggravate the no start condition.
1. Depress and hold the accelerator pedal to the floor and crank the engine for 7-8 seconds. (This will clean out any unburned fuel from the combustion chamber)
2. Release the ignition key to stop cranking.
3. Release the accelerator pedal and start the engine. If the engine starts while performing Step 1 the engine will rev up. Immediately release the ignition key to stop cranking and remove your foot from the accelerator pedal.
^ Do not keep holding the ignition switch in the START position over 10 seconds if the engine does not start. This may result in a weakened or dead battery.
^ Avoid racing the engine or sudden take off right after starting the engine.
^ If the engine still fails to start following the De-choking procedure, have your vehicle inspected by your Mazda Dealer.

for your info there is a recall for this problem. contact mazda.