Okay, I think I'm missing something here. Let me explain what I'm doing and then you might be able to see what I'm doing wrong. If you could, could you walk me through what I'm supposed to do to Compile Debugger helper after you read this?
Let's say I have a program that I'm writing called "Hello World". I open Qt Creator and start a new project. I tell the wizard that I don't want a GUI, it's a Qt4 Console App. After I write my code I go to Tools -> Options-> Qt4-> Qt Versions and I have an entry in the table called Auto-detected with a valid path to my Qt build and a red "X" under the Debugger Helper column. So, I browse until I find my MinGw Directory and then I click the "Rebuild" button. When it finishes, I still have a red "X" in the Debugger Helper column and I click the "Show Log" button and there are hundreds and hundreds of "undefined reference" errors.

I have done this same process for each of the applications I'm building and the result is always the same.

Thanks