If you can't identify the app, then there really isn't a lot you can do - and if it's being opened by a third party app at the users request then pretty much the only way to find it is to read the active windows list and look for changes. But...that will find every application the user opens, including Solitaire, Notepad, IE..., so isolating the one you want probably won't be simple.
And I'm not sure that you can "get at" the text output of a console app anyway unless your application is the one creating the process - I'm pretty sure that you would need to divert the output stream to you app via the
Process.StandardOutput[
^] property of the Process object.
What are you trying to do that you think this might be a solution?