iPhone 3G - Applications from Appstore issue

I bought the iPhone 3G and I've downloaded applications (legally) on the appstore.
Everything worked fine until I click on an application at random and the latter does not start.
The iPhone displays the entry screen of the application, and then automatically returns to the home screen.
What is the problem?

• Note that: I even deleted all downloaded apps and re-install them, with no success!

The problem comes from the protections of Apple Appstore accounts. Only the account used to download a particular apllication, will be valid . If you have two account this can be the cause of the problem.
This solution, requires no restauration

• Open iTunes, click on the Store option on the top, click on "Authorize Computer".
• A window opens and asks you to enter the Apple ID,and password.
• You plug the iPhone into iTunes, synchronize them, and everything operates again perfectly.
• Thanks to Malaika for this tip.