Good morning and thank you for posting on the Final Fantasy XIV Technical Support Forums.

If you don't have issues on the PS4 (I'm assuming they are using the same connection) and you can run the game using Windows 8 compatibility, then it is something specific with your PC. I'd suggest you check a few of the following:

The game will use the Internet Explorer web browser to connect to the internet. Open Internet Explorer, then open the "Tools" setting, go to "Internet Options" and adjust the following settings:
- Under the "General" tab, please delete ALL browser history.
- Under the "Security" tab, please move the slider to the lowest possible settings or no higher than "Medium"
- Under the "Privacy" tab, please move the slider to the lowest possible settings or to "Allow All Cookies"
- Under the "Advanced" tab, please make sure that "Allow software to run or install even if signature is invalid" is CHECKED.
- Make sure that all SSL and TLS (EXCEPT SSL 3.0) are CHECKED. [SSL 3.0 should be UNCHECKED]
- Hit "Apply" to save the settings, and then "OK, to close the Internet Options menu.
- Right-Click on the FFXIV launcher icon and select "Properties"
- Go to the "Compatibility" tab, and change the compatibility mode to "Windows 7"
- Hit "Apply", then "OK" to save the changes.
- Please RESTART your PC now. Once your PC has been restarted, Right-Click the FFXIV launcher icon once more and select "Run as Administrator"

Reset your router by turning it off for a few minutes, then back on.

Make sure your anti-virus/firewall has the appropriate exceptions for Final Fantasy XIV (you can temporarily disable them while you try to connect as well).

Make sure to use a wired Ethernet connection as opposed to a wireless one if possible.

We hope we can be of assistance in helping you enjoy the exciting world of Final Fantasy XIV!