Dead or not
 

I have a problem with my 05 base RX8 Auto. The other day Girlfriend started it and moved it into the garage. The next day it would not start. I have advanced knowladge of automotive, but not rotary. The battery is good, fuel system is new, and the starter turns. But engine will not turn over. I think it has to do with the ignition system. I have new ignition coils on their way. But I would to have a second opinion.

I wonder if it's flooded.
did you check for it?

If it is flooded there is a deflood procedure. But, also, a healthy car should not flood so the new coils are a good idea.

FIFY.

Stalled my 8 twice when it was cold. Never flooded it.

You will want to de-flood the engine using the de-flood procedure. You will then want to inspect and replace the plugs, wires,and coils if they have not been replaced in the last couple of years.This will ensure reliable starting.

You risk detonation and losing an engine if you shut it off before it warms up to normal operating temperature. I lost an engine on my 04 this way. I knew better but I was in a hurry and due to a very healthy ignition system, it did not flood the engine, but detonated due to raw fuel in the combustion chamber and ruined an apex seal.

Not dead
 

So, I did the deflood prosscess. For several hours total. Removed spark plugs top two were wet and black bottom two were just black. I cleaned them. Then, did the deflood about ten times. Putthe plugs back in and tried again. The start still wines but engine does not sputter or crank.
I am going to be getting new plugs and wires soon.
On a side note does anyone in the Houston/humble area that knows or can help with the removal and cleaning of the secondary shutter valve.

That's nor exactly the procedure, you're supposed to (with plugs in and all that) push the gas pedal all the way down and crank in 5 second bursts. After a few sets, try starting regularly. Repeat.

When you turn the car to ON do you hear the fuel pump prime? Possible it has failed, but a bit unlikely since you had no prior symptoms.

I've shut mine off heaps of times cold and never had an issue. Didn't realize there were any problems in doing so

She's Alive!
 

I got her running after a company meeting. So, basically I am super happy now and wanted to thank all of you for your help. I never would have thought of it being fuel flooded.
I am still having trouble with it running stable. And now there is a semi loud tick that is coming from the left rear part of the engine.
I am still replacing coils, plugs, and wires. And will be getting it coded to see if this caused some new codes.
Lastly does anyone suggest I seafoam her or not. Because, the original owner most likely didn't take proper care of her. There is a nasty carbon build up on the plugs so I could imagine what the rotor housings look like.

Carbon buildup on the plugs isn't great. Replace the plugs, coils, and wires asap. This can be why the engine isn't running well. Seafoam can help as a fuel system cleaner and can be used in a vacuum port to help de-carbon the engine. There is a procedure for this as well. If you're interested, we can help you with that.

Now, as far as the loud ticking, you could find that there is just a simple small exhaust leak or you could be experiencing rotor bearing failure. I had never experienced rotor bearing failure in any of my rotary powered cars until I bought my old Titanium Grey 05 GT. And I have owned rotaries since 1999. A lot of them. The engine in the 05 was ticking loudly from the rear of the engine and it ultimately ended up being a rotor bearing that had failed. A new short block solved the issue of course.