How are you trying to access the video? Have you looked in the gallery?
Also you can try downloading a file explorer app. I use root explorer but if you are not rooted look for file explorer in the app store.
You will want to navigate to storage/emulated/0/dcim to find video files recorded with the camera app that came with the phone.
Sent from my SAMSUNG-SGH-I337 using XDA Premium 4 mobile app
AT&T I337 Galaxy S4
NB1 Kit Kat Firmware
Work around Rooted (Thanks to all who worked on that method)
Galaxy Tab 3 10.1 GT-P5210