The Internet seems fine, as I can browse thru my iPad and also on the PS3. Any help?
Removing the game data for FFXIV and redownloading it may help:
If that doesn't help, the PS3 safe mode restoration options may be able to assist you:
Also, if there is any issue with the game or game servers, you should check the official site for more info:
When I make a connection test, it says that obtaining an IP address and the Internet Connection succeeded, but when it goes thru the part that says PSN it says that it failed.
One test you can try doing is to try to connect your console to another network, ideally with a different ISP both wired and wireless. If you can connect wirelessly then issue would point more towards how your home network is set up. If cannot connect to any network wirelessly or wired, they may be an issue with your console that needs servicing.
Did you try any of the Safe mode options?