I think I've figured out what's causing the problem. I had a DVD in the drive when I was booting up Parallels. Since I took out the DVD, I'm having no problems loading it. I guess it doesn't matter now, but I'm using Parallels with a Windows Boot Camp partition. I was getting the message upon double clicking to open Parallels. I'm running the most current version of Parallels, as I was able to update at some point last night.
Moral of the story: Don't run Parallels with a DVD in your drive. Doh!