In error report you got stuff in your Downloads folder.
Here you are showing Program files folder.
Although yes, you don't have rights to control those files (ownership) - blocks in Allow column should be checked/ticked.
(or move working/project files to a folder where you are Allowed with Full control)
Read this article and use script attached at the bottom, it should solve the problem.
Add "Take Ownership" to Explorer Right-Click Menu in Windows
I've got Downloads folder in the command window, because I have downloaded 2.72 version to check, if it will work, but normally my 2.76b version was inside Program Files.
Now I have unistalled Blender from Program Files and installed it inside my personal folder "Tomasz", where I'm 100% sure that I have full control, but still the same error appears. After using "Take Ownership" script, nothing changed, still the same error. Every path is correctly assigned and everything is in it's place (standalone, render_corona in addons folder). So strange...
EDIT: Also, is Corona Renderer supposed to work by opening "Corona_Release.exe" in standalone folder? Because when I run it, it stops working and gives me this error:
I am writing about that .exe file:
EDIT2: When I run "!run sample" batch file from standalone folder, it gives me this (it appears for a second and dissapears):
EDIT3: I am pretty sure I have found the reason why it is not working. I have read that Corona Renderer will not work with CPUs not supporting SSE 4.1 and my AMD Phenom II X4 955 does not support it. So I guess I have to wait for developers to make Corona Renderer compatible with my CPU or buy new one, which supports SSE 4.1.