When I try to launch my downloaded apps, nothing happen. What can I do to fix this?

Have you tried a Reset...

Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears. Release the Buttons.

http://support.apple.com/kb/ht1430

Also, See Here...

Troubleshooting applications purchased from the App Store

Try downloading any free app from the store (as that appears to reset something) and then re-try them - the free app can then be deleted.