Hello,
First you will need to verify that you are getting good spark. If you are, then you will need to remove the plugs and see if they are wet. If you have spark, and they are wet, you will need to unplug the coils and crank the engine over a few times with your foot floored on the accelerator to clear it out.
Plug the coils back in and get a new set of plugs. They are not cheap, so don't be surprised. Also be sure you install the leading {NGK REA7-L} and trailing {RE9B-T} in the correct positions. { if you are a slow driver, lots of stop and go's, or city driving, use RE6A-L for the lead plug. It is hotter.}
At this point, start the vehicle. If it cranks but does not start after a couple of starts, hold your foot to the floor. If it still does not start, remove the plugs and preform a compression test. If you do not have access to a Mazda tool, remove the fitting in the end of the compression gage. Hold your foot down to wide open throttle and crank the engine. Should show between 99 to 120 psi. If it is below 99, and I mean 80'and below, you more than likely damaged the APEX seal. This will cause the engine to have lo compression and flood.
Let me know if you need any further help.
Scott
ps. Not to scare you, but just in case.
http://www.rotaryresurrection.com/2ndgen/tech_engine_int_damage.html
ASE Certified Technician
Ase certified, 24 years, bumper to bumper all makes