Unable to copy file

I have a big folder in a Case Sensitive HD that I want to copy.

But, try as I may, nothing works. I always get a message halfway through saying that the file already exists and can't be copied since the target doesn't recognise case differences.

What can I do?
I want to reformat the drive to make it "case insentitive", but I need to have those files backed up first.

How can I copy them elsewhere?!?!?!?

EDIT: the "solution" seems to be compressing the files in a zip folder and then uncompressing to the desired destination. Still not the best procedure, though.

Mac Mini with Mountain Lion.

 

Same thing happens with a flash drive (I tried). I assume a CD would be the same, but haven't tried.
As I said, the only way to bypass it was to ZIP the folder and then re-open.

I understand the drives should all be case insensitive. That's what I'm trying to achieve now.

They were formatted case sensitive unintentionally. This is my first Mac and I probably didn't know that at the time. What's weird is that it should have been left at the default (which I'm told is NOT case sensitive), which I don't remember changing...