I do not know the details of Windows 8.1 (since I am using 7) and JRE 7 on Windows 8.1, but a PC firewall under Windows NT 6.x (such as Windows 8.1) can be eplained.
The first question is whether the PC uses the Windows firewall or a third party personal firewall. One thing must be clear on a Windows PC: use exactly one firewall at a time (otherwise the firewalls can obstruct each other).
If the PC has a so called anti-virus software or software package used OnAccess, then this can be a cause of problems for or beyond the pure firewall problems; I am assuming that no such anti-virus software (package) is used and any prior such software has been properly deaktivated and deinstalled completely. Otherwise, matters can depend much on a treatment of that software.
So given a use of only the Windows firewall, then next things to be checked are: is it activated for the current PC settings; is only Inbound or also Outbound activated; are special rules added to the default rules?
If also Outbound is used or if Inbound has special rules, then one must check whether KGS IPs / URLs and ports are allowed.
http://senseis.xmp.net/?KGSIssueFirewall