I don't understand why I can't take photo or video with my Samsung Galaxy S4. I have 32 GB of memory and I haven't a lot of photo or apps in my mobile phone. I tried to delete photo, video or apps that I don't use, and also I have just restart my phone but the situation is the same.
Speaking with experiance with a galaxy S4.
Try deleting the cache, from the storage menu. Goto Storage->Internal Storage-> Delete Cache
Should empty up a lot of space by now, for more storage,
Goto Storage->Internal Storage-> Explore
Delete files named,
These are temporary files created, you can delete them, it won't harm any of your data.