Whole car shakes applying power in 5th and 6th
 

I have a 2004 6-speed manual, and when I apply power in 5th or 6th gear something shakes extremely harshly under the hood and makes the whole car shake. I don't get any power either while it's happening. I'll post a video later when I get out to the car.

I have seen bad U-joints in the drive-shaft cause this problem on other cars. I dont think U-joints are a common problem in the rx8 though. Worth a look though.

it could be a bad wheel hub assembly. Have you removed the front wheels and checked the upper and lower control arm joints and bushings? Inspect the boots of the ball joints for damage such as rips or tears. Check the outer tie rods for excessive play as well. Inspect the rear driveshaft as well, because the u-joints could be a problem as mentioned previously in the thread.

Would those be an issue in only certain gears, though? I can drive hard all through 1-4, but as soon as I apply moderate power in 5 or 6 it all shakes and I don't get any power.

First and foremost is check the driveshaft. Then the CV axles. Those, excluding and engine problem, are the only things that should give you a drive line vibration

Well, if it would help you out, Chris, I can take a look at it for you. If you happen to go to the Daytona area, you are more than welcome to come over to my place and I can check it out. You don't have to pay me, just trying to help another club member. The only way to truly see what is wrong is to inspect the undercarriage components.

I might take you up on that. I'm over in the UCF area, so it's only an hour or so.