I'm sorry to hear that you're having trouble. Provided that you replied to the automated e-mail, you will receive a response eventually. My support response time has been 5 weeks for the most part. Hopefully you opened separate tickets for different issues, since opening duplicates does nothing but clog up the overloaded support system even further (and it sometimes
confuses support agents too).
If you're trying to play InfraSpace but you can't log into GOG Galaxy, consider getting
the offline installer and playing it that way. The game doesn't have achievements (at least not yet), so you'd only miss out on playtime tracking.
For the issue of not being able to login itself, double-check that GOG Galaxy has Internet access through your firewall. There are many executables scattered throughout
C:\Program Files (x86)\GOG Galaxy and
C:\ProgramData\GOG.com\Galaxy\ If that's not the source of the problem, you can try a clean install. Uninstall, then move
%LocalAppData%\GOG.com to another location for safekeeping, then install from
the full installer.