You double posted the thread so I'll give you a double answer.
Probably your best bet to begin diagnosing your problem would be to take it down to the Mazda dealer and have a compression check done (rather than chasing a bunch of silly stuff around in circles). Usually a couple hundred dollars, depending on the dealership.
The most common problems with the first generation RX-8s that I have heard tell of are low compression, a less than stellar ignition system, and a crappy starter. It could be any of these, but the low compression would be the most serious.
To repeat what has been told to me by people that rebuild these things regularly:
Low compression, this would require a rebuild if it is the problem. The first gens had insufficient oil injection to the rotors in an attempt to cut down on oil use. Bad idea as rotaries require oil just like a two stroke. Easiest fix is to premix 2 stroke oil with your fuel to give it a little additional lubrication. The shorter apex seals didn't help things either.
Most people upgrade the coils as the stock coils were marginal when new and get worse quickly.
The starter did not spin fast enough and has also caused hot start issues. The fix for this is to use the starter from the 2nd generation 8s. Pricey, but worth it. So I've been told.
caveat: I don't own an 8. This is what I have been told by those that work on them regularly and what I have seen others struggling with. We'll see if I get any arguments from those that actually own one.
