I bought A 2004 Mazda rx8 2 weeks ago and I go out this morning to start it and it cranks over but doesn't catch ? What do I do ?

 

There are lots of reasons for not firing. With all the information you have given us, all of them are possible options.

Battery
Starter
Engine Compression
Coolant seal
Spark Plugs
Plug wires
Ignition Coils
Grounding
e-shaft sensor
fuel pump

and with nearly all of those, a failed start means flooding on top of any of the other issues.


What inspections or testing was done when you purchased it?
did you get a compression test like you are supposed to?
have you any idea of prior maintenance?
are the ignition components at end-of-life?
are you smelling raw fuel from the exhaust?
Coolant from the exhaust?
battery tested?
starter tested?
do you know your crank speed?
Mileage on the engine?
Mileage on the car?
Which transmission?