I upgrade from a galaxy 3 to an s4 and my sd card when I transfer everything it didn't go through so I went back into the phone memory got all the pictures but none of the videos came up on my SD card and I can't find the videos
Try to connect your phone via usb (computer...) and search inside. There should be a folder with your videos!
If you want to transfer data... the easiest way is to use a computer Just cut/paste (backup is reccomended).
p.s. When you plug your SD card into a new phone... save your data... then format it and insert it blank!