Checking the PSU cant hurt, boot up a torture test to exclude it being just a FFXIV issue or not.

A stab in the dark is the GPU on the way out though, give its issue with a monitor and the artefacts, had a 8800gtx went out with funky screens going all green/purple. but def best to check rather then jump to a conclusion.
Does the monitor show up via the 2nd gpu ok?