This kind of issue takes place when something - usually security software on the client's end - is blocking Galaxy from contacting our servers.
We are aware of this affecting systems which are using firewall that use a "scan secure connections" feature. ESET is one such firewall - please make sure to disable this option in order to resolve login issues.
Generally, you should make sure that your security (anti-virus, anti-spyware, firewall etc.) software isn't interfering with GOG Galaxy. To do this, make sure that GOG Galaxy is added to the software's trusted applications list (how to do this varies, depending on the security software). Also, please double check that you are not blocking connections with our service - *gog.com*, especially *auth.gog.com* and *login.gog.com*.
Make sure to check in case you are using multiple firewalls, including those installed on routers and similar networking devices.
Lastly, make sure that you have all essential Windows Updates installed. Some of our users have reported that their systems were outdated, and installing updates solved this problem.