iPhone 4 apps won't open?

When I click on the app, it looks like it's going to open but then quickly goes back to the screen. I've tried turning off my phone, restarting it, and resyncing the apps on iTunes (where you check and uncheck the apps). Because I downloaded most of my apps on my phone, not the computer, the checking on iTunes only fixed the apps I bought on iTunes. I'm currently downloading the new update, 5.1.1, but still have 2 hours left. Will this fix it? How can I fix the apps I bought on my phone? Thanks!