Today, I started KDE and for some reason Compositing was disabled, and my System Settings icon was missing from its normal place in the KDE Menu. I could not re-enable Compositing. I suspect the problem is because of some recent software upgrades I loaded for KDE 4.4.2. Here is how I fixed my problem. Hopefully it will help others.
To make sure there was no problem with my computer, I did a simple but easy test. I created a new user through KDE's system, and logged into that account. Everything worked fine. So, I knew it was a configuration file problem.
I could now compare the new account's config files (which reside in the an individual's home directory and typically start with a '.' or are stored in a directory starting with a '.'). Comparing the new account's config files against my own. I was able to eliminate quickly all of the non-KDE config files fairly quickly.
I made a backup of the .kde/ directory in my home directory, using a tar file. Then that directory, I used a simple divide-and-conquer technique for finding the troubled files. Instead of checking the over 100 config files from my directory, I simply copied the first half of the new account's config files over my own, and logged-out-logged-in to KDE to check if that fixed the problem. If not, I tried the other half, and repeating the eliminating half until I found the files the troublesome files.
The files in question was all prefixed with kwin. Had I guessed intelligently I would have tried these first. But simply overwriting all the kwin related files in ~/.kde/share/config/ with the newly created account files (which were probably created from defaults) fixed my problem. Compositing was restored and all I had to do was reset a few minor customizations I had before.