But when i close that box without giving any correct activation key and re run the application, it directly starts the application.
This isn't a bug in TurboActivate. It's a bug in your code -- you're not handling the responses correctly. If you want to close your app if the user doesn't enter the correct code, then do that.
Specifically use the IsActivated function to determine whether the user is activated. And if they aren't, then either disable the features of your app, or close your app (or do whatever's best for you and your customers).