Gallery has no storage location.
When you restart the phone, Media Scanner scans the phone and any SD card for media files and builds a database. Media apps (like Gallery) use that database to find files to display. (Sound apps will look for sound files, video apps will look for video files, etc.)
If you moved the entire folder to your computer, you deleted it on the phone, so the camera app can't store its pictures anywhere. You have to have a /DCIM/Camera (case counts) folder, or open Settings in the camera app anf change the location it stores pictures to. (It'll create a folder if you tell it to store in one that doesn't exist.)