What messages does the application produce when it crashes? How does the crash manifest itself?
Root typically has much stricter controls in place on a variety of commands to reduce the possibility that an administrator will hose over the system. For example, deleting files often requires confirmation, graphical logins are disabled, and whole groups of commands may be removed from the execution path depending on how console login is performed.
It's impossible to pin down what's going on, though, without some actual information on what you mean by "the application crashes". One likely explanation, especially since you're rebuilding Qt yourself, is that the root account can't find Qt's dynamic libraries. But that's just speculation. Send some error messages.
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