Like many others, I have run into the "Unable to Connect to Background Process" error when trying to submit video files to the Compressor utility. I've looked all over the net, including the Apple web site for a fix and found nothing truly useful. The best Apple seemingly can do is to ask the user to reinstall the software.
After many hours of reading and testing, I think I have found the fix for this problem. When you install Final Cut Pro HD 4.5 with Compressor, at the end you get a message box asking you if you would like to fix Qmaster. You would think that this would fix the Qmaster problem, but it doesn't seem to do so. This is the reason that you get the background process error message -- the Qmaster process is not running in the background, and this is what Compressor needs to work properly. What you can do to get it working again is run this command in a Terminal window (you will need your admin password):
sudo /Library/StartupItems/Qmaster/Qmaster start
This will only work until you restart your computer again.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20051017072758916