I solved the problem and, pardon my French, it was just too bloody easy.
As a result of someone somewhere mentioning that he saw the Automator Launcher in the Activity Monitor, I fired up both atMonitor and the Activity Monitor. Sure enough, the Launcher was running but inactive. To see what would happen, I tried running the service from the contextual menu, and the Launcher showed no surge of activity whatsoever in either monitor application. I decided to kill the Launcher process, whereupon, it seems, every pent up and unexecuted automator process hung up on the Launcher ran, with all kinds of messages popping up on my screen. (God knows what I did to my computer!) Anyways, all my services seem to be working again.
In short, if you have services that run okay in Automator but do not run on their own outside Automator, you might want to check your processes for Automator Launcher and kill the Launcher process if it shows no activity when you try to run a service outside Automator. It worked for me after trying every other suggestion I could find.