Ok, so the number 4 cylinder won't fire and I know this because the engine sounds inherently unbalanced (like a boxer engine) the one exaust header isn't as hot as 2 and 6 and, if you unplug the coil pack it doesn't change how it runs at all...
I know it's not the following
A. Coils, I swaped them around and the problem stayed
B. Spark plugs, I replaced, and swaped, and look it out and put it into the coil and you can see it arcing...
C. Injectors, I switched 2 and 4 and again no difference

And it has good compression btw...

Please, please help, I have never had this much trouble diagnosing a car!!

 

If your sure compression is good i would look into wiring. The coils are a 3 wire system meaning there will be a constant 12v power and ground then there should be a signal wire for the coil to fire. Im guessing you have a power ground or signal issue to that coil. Check the harness connectors and look for loose or damaged pins/wires. If that all checks out then there could be a bad coil driver in the ECU. This is pretty rare but could happen. Good luck.

 

Are you 100% sure that the coils 4 and coil 6 wiring is installed correctly...when you look at the loom if you re-install them logically they are backwards...I would suggest labeling all those wires

 

Did you figure this out? if so you can stop reading. If not There is another possibility... The ignition coil condensers have dealt a few people problems in the past. But usually when the condensers go bad it will fry/melt the ignition coils. It is a 2 wire capacitor that is taped up in the main engine harness on the ground side wires of the ignition coils.