I turned on debugging but the darn thing still doesn't show up in the devices list.
For reference, I'm using the cable that came with the Note and I can transfer files successfully
Have you installed proper drivers or the Android SDK? If you get Android SDK for your pc, make sure open up the manager in there. Then download platform tools and tools. It should give you needed drivers and support for ADB & Fastboot(not sure if Samsung uses it).
Or you might be able to use Odin to do whatever you trying to do with ADB. Not sure though. Depends on what you trying to do.