It seems that you're using an outdated browser. Some things may not work as they should (or don't work at all).
We suggest you upgrade newer and better browser like: Chrome, Firefox, Internet Explorer or Opera

I get the error message "you have no access to this product" when I try to download The Witcher. The GOG support team has not gotten back to me. Has anybody else had this problem?
That's weird. I have not experienced this. Does it work if you try to download it with your browser? Do you have any other games from GOG, and if so, do they work in the downloader?

One other idea is that you might have problems due to not being logged in as administrator. Can you try launching the downloader as admin (right-click it, then pick that option from the menu) and then downloading the game?
I have re-donwload it two weeks ago without a problem. I have used the browser not the downloader. May be you wanna give it a try.