Curious if maybe it has been set run in minimized mode? This could have happened if you were trying to set compatibility/Admin options on it. If you did so, go back and make sure it isn't set to run minimized. It's been known to happen by accident or from Windows freaky random file corruption.
May be a long shot... but lets also take a look at your display settings, just in case it is a simple matter of an error in the config file tripping something up. It is a plain text file that you can open with any text editor like notepad, wordpad, textpad, etc. It is called FFXIV.cfg, and nested a few levels into your documents folder. Depending on your view settings, you may not see the .cfg part, but just FFXIV (there will be one called FFXIV_BOOT.cfg in there as well).
Open your file browser and drill down your folders along a similar path to this location:
C:\Users\<Your Windows User Name>\Documents\My Games\FINAL FANTASY XIV - A Realm Reborn
Right click the FFXIV file and select "Open With...". Depending if you have opened this file type before or not, you may see something listed already or you will need to pick one to open it with. Notepad will do just fine. About 18 lines down, you will see a section for the display settings. It should look similar to this, though the dimensions may be different:
Code:
<Display Settings>
MainAdapter
ScreenLeft 142
ScreenTop 61
ScreenWidth 1600
ScreenHeight 900
ScreenMode 0
FullScreenWidth 1920
FullScreenHeight 1080
Refreshrate 60
Fps 0
AntiAliasing 0
FPSInActive 0
ResoMouseDrag 1
MouseOpeLimit 0
LangSelectSub 0
Gamma 50
UiBaseScale 2
Make sure the dimensions set for both the Screen and FullScreen lines are valid values (not larger than your screen supports). Make sure it is a "standard" size set for the FullScreen values--sometimes game engines get weird if it's a custom size. The Screen lines are used for the windowed modes, so make sure they are also a standard size if you were stretching a borderless window to full screen. I've seen some cards drop a screen to the taskbar if the window goes too far out of bounds to the screen or the card's native resolution limits. You can see the more common dimensions in this chart (use the URL if the pasted image isn't clear enough to read):
http://en.wikipedia.org/wiki/Display...Standards8.svg

Once you've confirmed the dimensions are proper, try setting it back into windowed mode (make sure the dimensions are smaller than your full screen dimensions, to make sure it is actually windowed) and then changing the value of ScreenMode to zero like it is in my example to make it go back to windowed mode, than save the file. Hopefully that will get it to load in a normal window so you can set options back again with the GUI.
There could also be something funky in the driver level options (AA, refresh, etc) that is causing it to freak out. You can set some of them manually as well by directly editing that config file, but do so at your own risk. Some options should be pretty obvious because they are simple on/off toggles, but others may have a range of values and you may get strange results without knowing what 1, 2, or 3 represents. As a last resort, you could try resetting things to defaults from the launcher (buttons at the bottom, Configuration). Make sure to make a backup first though, as it may reset all kinds of things you won't want to spend a lot of time redoing.