Okay, so I'll drag an image / footage / music into the project, and it'll be fine.
BUT, when I drag it from the project to the composition, I get the spinning wheel of death (I'm on a Mac).
By the way, I'm using After Effects CC 2014. If you need any screenshots, of if I'm being confusing, let me know! I've been using after effects for two years for my own personal use, yet I still know nothing about the terminology or troubleshooting.
Start by providing exact system info and details about your footage, comp settings and so on.