My 2004 Civic LX coupe has been throwing misfire codes for a few months now. It also idles incredibly rough. I can unplug the coil and/or the injector plug on cylinders 2 and 4 and it doesn't make it idle any worse. I started at the spark plugs and coils and replaced them all, no change. New air filter, no change. I pulled all the injectors and cleaned them the best I could and rearranged them and still had 2 and 4 misfiring when idling. I should note that once you give it some gas it smooths out. I sprayed throttle body cleaner into the throttle body and cleaned that the best I could without removing the entire thing. Finally I moved onto a compression test and I get 210, 210, 210, 110. Looking around on here it looks like the consensus is around 135 is normal. 210 is obviously way too high. I replaced the timing belt last year when I got this car as I believed it was on the original one and it had around 165k on it, 185k now. Could it have slipped? Is it a burnt valve? Not sure where to go from here. Any suggestions would be appreciated.

 

I'm not sure how you're getting such high compression on the other cylinders, unless someone installed some high compression pistons before you got the car. If that's the case, you'll need to be running high octane fuel to get it to idle correctly.
If you can get access to a borescope, I'd take a look inside the low compression cylinder and see if there is any coolant, oil, scoring on the cylinder wall, or a burnt valve.

 

Mabye the cylinders filed with liquid, Like a leaking injector or coolent