Are you asking how to troubleshoot a No-Start on an RX-8 or are you explaining how to fix it?
If you are talking about the Flooding issue the RX-8 has, the problem stems from the driver. RX-8's having the 13B Rotary Engine as opposed to a traditional 4 cylinder, operates a bit differently.
The Rotary Engine needs to warm up before it can be turned off or else you will flood the engine and cause it to not start for 2 to 15 minutes.
The RX-8 is not meant for quick runs down to the store and back while shutting the vehicle off in between. If you are making quick pitstops here and there on your daily trips, leave the vehicle running, or wait until the engine gets up to operating temperature before shutting it off, so it will burn off excess fuel instead of letting it sit inside and flood the injector ports.