I see that the last time you ran Autotune, it was for 6.0.3, which was released a year and a half ago. That version is extremely outdated and will actually no longer work for some social networks such as Facebook anymore, as their API's are constantly changing. I'm not surprised there are issues.
Generally a blank page indicates a PHP error. Please turn on Error Reporting in the Joomla Global Configuration and let us know what the error is. If it's something obvious, that can help narrow down the problem. However, as I mentioned a very old version is likely to have other issues, even if we help you to get through this one.
-Melissa