I finally decided to try Acronis True Image. Now it takes longer for my system to boot after reaching the desktop. The desktop and taskbar display, but I can't open applications or browse My Computer for a significantly longer amount of time than before installing Acronis True Image.
To troubleshoot, I uninstalled Acronis, and the problem disappeared. Then I reinstalled it, and the problem reappeared. I now have the processes TrueImageMonitor and TimounterMonitor disabled at startup, and that's cleared up the problem too.
Many people have recommended this app (even I did since I trusted those who did), but I'm a little concerned about this new problem.