I also had same problem, i tried to use all the possible solution posted on this thread, but i found out i had same problem as JohnnyFun explained, but as per HenrikB solution i could not find any settings option in my Samsung Galaxy S6 phone ( Android 6.0.1)
Settings -> Storage -> menu -> USB computer connection
I finally figure - when connecting my phone throught charger in pull down menu i see options like -
Then click on "Connected for chargin " >>> you will see options like >>
Over there you can change option to "Transferring media type files"