You might have to "deactivate" the old PS3 to transfer your licences for DLC, PSN bought games and possibly the licence key for FFXIV.
Check your regions Playstation website support guide for info.

I had to deactive my PS3 last year before sending it back to the shop, basically it desync's your account from the PS3's hardware ID (as you can register 2 PS3s per PSN account) so you can keep bought/downloaded/licenced key'd content.
Re-sign in with your PSN ID on the new PS3 and make it your primary console - sorted.

Again double check on the PS website for your region for instructions.