If you really don't use sonic then uninstall that, as it might be causing a conflict. If you have to uninstall Icopy to burn your stuff, what exactly are you using to burn btw?
Icopy is a ripping program right, and I take it it has a burn feature? Are you ripping dvd's or just cd's as you mention above?
For ripping dvd's I'd recommend dvddecrypter with anydvd running in the background, or dvdshrink. For burning I use Nero myself, but I believe too many burning programs installed can screw things up, as you have apparently learned.
More information would be good. I'm sorry, but your post is a little confusing to me in relation to distinguishing between dvd and cd's and ripping and burning. If you describe what exactly you are trying to achieve it would be easier to suggest a solution.