In the responsehandler.php file where exactly am I looking because I can't find something that is set higher than 644?
I'm lost right now in there and confused.

It's not inside the file. It's the file itself. I'm not sure how you get to your Core files, but if you do it via FTP...just right click on the file name and the last choice on the list is 'file permissions' or something like that. Click that and a box will pop up with all these little boxes: write, read, execute. Click them on or off until the number at the bottom says 644.