I have a Samsung Note 3. For the last 2 months, I can download APK files - for example, just downloaded the new Google Play Store here: http://www.androidpolice.com/2014/10/09/breaking-google-play-store-update-5-0-31-adds-even-more-material-design-highlights-and-moves-whats-new-to-the-top-apk-download/ and it's on the phone, but when I open it and go to install it, when I touch INSTALL - nothing happens. It's there, but it won't install. This happens with any APK. one caveat: in the past if I've rebooted into safe mode - which of course means with no downloaded apps running - then and only then can I install. Some 3rd party app might be blocking me from installing. That's all the info I got. Can you help?
I had a blue light filter app running that dims the screen to prevent damage to your eyes, and it was apparently blocking the installation of APKs and the selection of certain menu options in other cases.