Based on reading this thread, I went to the Apple Store at Grand Central Station today. After scanning the crash reports in Diagnostics & Usage, the Genius said I have serious software corruption. This is due to my failure to turn off my iPad on a biweekly basis. (I've been keeping it in Sleep mode since I bought it two months ago.) I have to install a brand new operating system, and I can't restore from iCloud because the problem also exists in my backups. First, I have to copy my songs, videos and photos to my computer. Then I have to make sure that important files for essential apps can be downloaded from the developers' websites. As long as I have a username and password, I'll be able to this. If I don't have these two things, I need to export the data by other means, e.g., via email or to another cloud storage service like DropBox. She then gave me instructions for starting over. Once done, after I get the welcome screen, I have to unplug my iPad to prevent it from syncing to iCloud and select ”Set up as a new iPad." I have my work cut out for me because I have three years worth of information in a variety of apps, but at least my problem has been solved—thanks to all of you in this thread.