Uhh, can you be a little more specific? It could just be a temporary thing, just keep trying.

2 day in the row this problem
I tried to add an exception to the antivirus

So, you haven't been able to log in from the client in two days?

Are you on a windows system? You could try adding an exception on Windows Firewall as well.

Edit: And yeah, giving us more info would be helpful.

Edit:
Never mind. I didn't notice the screenshot.

Add exception kaspersky, system win10 Log in

Okay, do you know how to add an exception to the windows firewall? Assuming you don't.

- Right click the start icon, and select the Control Panel option.
- Go to "System and Security".
- Under "Windows Firewall, select "Add an app through Windows Firewall".
- In that list, see if you can find GOG Galaxy Client.
- If you can, tick all the boxes beside it.
- If you can't, Click on "Add Another app", choose "Browse", and navigate to the GalaxyClient executable, and give it the necessary permissions.

I'm assuming this is going to fix your problem.

As you mentioned kaspersky , reminded me that Kaspersky has a IIRC white list feature where you have to manually add galaxy. (was in the alpha tests of Galaxy)
And to be certain that it is your AV, disable it for a moment and then try to connect, if it works, it IS kapersky.

Click on that blue "CONNECT NOW" button.

Just a shot in the dark...