In my experience, there's basically two common causes for instant reboots of a machine.
-- Insufficient power (power supply can't sustain load)
-- A very fast bluescreen (when Windows is configured to automatically reset on failure)
Try this:
Start > Control Panel > System > Advanced System Settings (left pane) > Startup and Recovery Settings > uncheck "Automatically Restart"
*If you still have instant resets on loading FFXIV:ARR, then I'd suggest trying to run Prime95 with inplace FFT's at the same time as Unigine Heaven (at max res, tessellation maxed, etc). If it's power related, most likely Unigine + Prime95 concurrently will cause the machine to instant reset too.
(these are two great stability testing tools in that they cause very-high load / will get your machine close to its limits on power consumption)
For your reference:
http://www.mersenne.org/freesoft/
http://unigine.com/products/heaven/
It'd also be helpful to know the make and model of the supply you're running.
--Essentially I'm not convinced that it's not a PSU issue, unless you've run some max-stress tests of that machine already (beyond what most games will do).