Hi Graeme,
I'm only slightly more technical than Mary. My first suspicion would be that the path you have entered has a typo. Here's the path on my local host. I'm using Win 7 Pro.
C:\gs\gs9.07\bin\gswin64c.exe
Note the "c" in the executable. In my localhost gs version there is another executable without the "c" at the end. I gather you should not use the non-c exe.
You also want to make sure there are no spaces at the beginning or end and none between the items in the path.
It would be best to actually show the path you are using and the path your host confirms is the correct one so we can all see them, if that isn't a security violation.
A slightly wilder thing to consider might be that, if you're working on a Windows server perhaps the path refers to some kind of Windows "shortcut" that php doesn't know how to recognize.