Your application authorisation is failing.
Reconnect to iTunes and sign into the account you purchased your apps with.
Sync your iPhone a final time, disconnect your iPhone once sync is complete,
restart (hold home and sleep buttons until you see apple logo), re-try launching your apps.
You should now find your application's launch flawlessly.
The reason this happens is because when you launch an application, it checks the account it was purchased from was signed in (on physical iTunes Mac/PC) on the last device sync.
If it was not, the device thinks the apps are being used by someone else other than the account holder. The safety mechanism in place for this, is for the application to crash on launch -
making your apps redundant until you can authorise your use for them.
Hope this helps. Any further problems, feel free to ask away ...
R-Fly