Upload an APK to a non-rooted galaxy s4 mini
First, do you have unknown sources checked under Settings --&gt; Security???
Also, have you tried another APK? If it is one you, or someone else developed you may need to uncheck Verify Apps in that same spot.

Second, do you only have windows? I don't know about permissions on Windows, but Linux requires sudo adb install or adb install as root user... actually any use of adb requires root or sudo permissions.

Second, does it just say failure? Does it say permission denied? Have you ever had that app installed before? 


  adb install application.apk


will give a failure response if you have a left over /data/app-lib/application folder or /data/data/application folder, or if you copied the apk to /data/app first without installing it, and then try to install it with adb, because the place is taken up already. 

If that is the case try (reinstall flag):


  adb install -r application.apk


You should also try (install to sdcard flag): 


  adb install -s application.apk


or last:


  adb push application.apk /sdcard


and then install from sdcard with a file explorer, or package installer.