Ok, I have tried to set it up so that I was following exactly the install instructions as they explain to copy all of the unzipped files to the server at http://my-domain/ which I have done so as to test to see if the issue was the testing directory. Same problem - blank screen in browser.

just to be clear, all of the files and directory's unzipped originally on my local computer have now been uploaded to http://my-domain/ (i have temporarily moved the existing website files so that the only files there are the zencart files).