I'm a member. When I press the rent disc option, it automatically adds it to my rental list. Films not out yet are added to the bottom. No idea about the drag disc option, never used it.
Doesn't really help you find out why yours doesn't work though!
not sure why it shows as empty, but you won't get anything with 3 films chosen - I've always had to have at least 10 titles chosen so that if one isn;t instock they can send another. try that.