I had this problem also. For me it was related to the UAC settings. I believe that you need use your Windows Live account to sign into Windows 8 or the Apps in Metro won't work so that is the first consideration. Turning off UAC can also cause this problem but not in my case. Read on for more information about this problem.
I set my UAC to off right after I installed Windows 8, the Apps all opened and stayed open for me however, when I turned UAC back on again most of the Apps would not open correctly and it would go right back to the Metro start screen. Nothing I did after that point would fix the problem. Turning UAC back off did not help. Others said that just having UAC off was enough to cause this problem but that wasn't the case for me.
Luckily I created a system image last week using Windows 7 file recovery in the control panel. I used that image to go back to before the problem started and the Apps were fixed, apparently this is yet another Windows 8 bug.
Lesson learned, do not mess with UAC once you have turned it off because if you turn it back on there is a good chance the Apps will not work again.
There are various complaints about this obvious BUG all over the internet with no clear resolution. Some say that creating another User account and switching back and forth deleting the old Admin account and a bunch of other screwy stuff, way too much of a hassle and likely to cause even more problems,...no thanks. Using a system image and not touching UAC again was the only way to fix this problem for me.
I have tested this three different times and it did the exact same thing each time. No more messing with UAC for me.