I've done a bit of research and this is what I found:
Sites aren't being blocked by IPS, I have used Opera with VPN on the other computer at home (in the same network).
I use ESET 9, but even if I turn it off (disable firewall and 'protection'), Opera still doesn't open https sites.
Uninstalling, reinstalling, cleaning, unblocking 3rd party cookies etc doesn't help.
I looked into flags, but I haven't found anything helpful.
Anyone, anything? What else can affect the connection?