2005 Cobalt 2.2L Random misfire code, rough idle, won't get out of it's own way.

corroded battery and ground, stirring dirt into the soup. Hose everything off and pay attention to the ground connection to the chassis...that one's gotta be clean...and the connection to the engine too-

If you scanned the OBD and got a 'random misfire' code that's a pretty vague fault. It doesn't know which cylinder is misfiring or why. Is that the only fault it showed?

Since you did all the things mentioned and I know that engine, remove the cam cover and check the cam timing. The timing chain could have jumped a tooth and it would run like that. My Jeep ran like poop when the chain jumped a tooth.

http://chevroletforum.com/forum/cavalier-12/2003-ecotec-timing-chain- issue-pics-48024/

http://www.fixya.com/cars/t9299891- looking_2_2_ecotec_timing_chain_diagram

http://www.ecotecpower.com/forums/read.php?f=6&i=1584&t=1584

I've heard the ground issue a couple of times since I've been dealing with this car. Will check that out.

No other codes. I have also been told that one injector on this engine could cause the random misfire code, but the injectors all sound the same with a stethoscope.

A bad injector will cause a specific cylinder misfire. I had one. I thought it was a clogged injector and tried fuel system cleaner. The rich mixture took out the upstream O2 sensor. --- All injectors clicking is good. If you check the injector coils with a meter, they should read around 12 ohms.

This engine has been known to have a random misfire code for one or more bad injectors. This has been a problem GM has been dealing with. It's one of my customers and I am not keen on replacing injectors without being sure.