I usually leave myself logged in 24/7 to my Fedora 20 system but recently, I went on holidays in Europe leaving house-sitters so logged out.
When I returned on Monday, I found that I could login to a tty and to ssh but not to KDE.
As soon as I entered my password, the Fedora page appeared for a second then the screen went black then returned to the login page.
Eventually, I thought to check my .xsession-errors and that indicated that libproj.so.0 was not found.
Installing that library fixed the problem.
(No idea why KDE would need a projections library.)
HTH, Stephen