Are you using any web browser extensions/addons that might possibly be blocking content on GOG.com? I have had problems on the GOG website before that happened until I allowed the correct things to pass through RequestPolicy, NoScript, and CookieMonster.

Avast antivirus is known to detect false-positives in some of the executables from GOG.com from time to time. This is a problem with Avast and if one encounters it you either have to allow the GOG content through and trust it, or you have to wait until someone submits the executables to Avast to review and they add them to their database as exceptions. If you ask GOG.com support about this they will basically tell you the same thing and it's ultimately up to you whether you trust GOG.com more or Avast, or what your personal risk gauge is.

If you get a notice of a problem with something from Avast and you're not comfortable to allow an exception, then you should contact GOG.com support for direct assistance as they have the best support in the industry. They may or may not be able to help you but if they can they will.

I would not recommend using Galaxy client as suggested however as it is beta and not ready for general purpose use. If you're already having a problem and try beta software and have problems with it too - which is likely, you're more likely to be even more frustrated. Just contact GOG support and if you can't get a solution to your satisfaction, then in the worst case they might give you a refund if you choose to go that route.

Another option to consider is to try a different web browser. If you're using Firefox, try Chrome or vice versa, or even Internet Explorer. You might not be comfortable with doing that but it is an option at least and sometimes that may solve the problem so it's at least worth a try.

What we tend to see in the forums here though is that most of the problems people have downloading are due to either:

1) Web browser plugins interfering with the proper operation of the website.
2) Antivirus or other security software interfering with downloads or interfering with the web browser being able to pass URLs through to the GOG Downloader ( gogdownloader:// links )
3) Restrictive firewalls that are not properly configured to allow the traffic through.
4) Systems that are infected with malware or viruses that might interfere with the browser or downloading etc.

There are other possibilities too of course and you may not be experiencing any of the above but the instructions given pretty much work for everyone with a normal setup so there is likely to be something unique to your setup that is causing things to not work correctly and GOG.com technical support is probably more adept to help resolve the issue as they do that sort of thing all day long pretty much. :)

Hopefully you can resolve the issue soon though, I know these sort of things can be frustrating. While our community tries to be helpful to newcomers having problems we might not be able to find a solution that works so again GOG.com support is the best approach if you can't resolve it on your own.

Hope this helps.