I have had this on-going issue with this CEL. Yesterday I decided to make sure I didn't have a broken wire going to the APV motor to the computer. All 5 wires checked with continuity. But, as soon as I clear the codes the second time I crank the car the light comes back on. I have even bought another motor for the APV and that didn't help either. I have tested the APV motor via 12v and spins fine and the little white gear spins very easily and freely. But, I heard the APV cycles when you turn the key? If this is true mine doesn't do that.

Any help and suggestions?

 

if you are positive that everything works (wires/apv motor), then there is something wrong with ur pcm

yes, the PCM does cycle everything at startup (make sure it is not stuck)

 

Not trying to nit pick but I can't find a P2004 in my Workshop manual or the one from Foxed.ca
That said I do see a P2004 in the Technical CEL thread on this site.

The the CELs I see in the list are P2006 and P2008 for the APV motor control circuit IC problem and/or APV motor control circuit/open

I would double check your CEL to make sure you are actually troubleshooting the correct problem.

Look up the troubleshooting for P2008, as P2006 is basically what NYCGPS said .. your PCM is baked.
http://foxed.ca/rx7manual/2003mazdarx8/

 

The code is for the PCM thinking the APV assembly is stuck in the open position. So in addition to checking the APV motor you have to also see if the APV mechanical assembly will move or not, is hard to move, or is not the problem. If the APV was stuck open, then you pulled and ran the APV motor, the motor will cycle to the closed position. If the the APV mechanical assembly was in the open position when the motor was installed in the closed position then it will never work properly regardless of whether it's stuck or not.

You will have to see if the APV gear will turn and cycle the APC mechanical assembly back to the closed position. If it will move, but has too much drag (which causes high load on the motor which is what the PCM monitors to determine this CEL code), you will have to figure out a way to resolve that problem. Unfortunately the only 'easy' way to remove the lower intake assembly to fully access and clean the APV barrels is to remove the engine from the car. Maybe there are some other ideas people can suggest to address it, but first you need to get to the APV gear that the motor turns and move it manually by hand to se what may be going on there.