In looking at iCloud's Help on my computer, it says that you have to create an iCloud account before you can activate it on applicable devices.
Set up iCloud on your devices
Before you can use iCloud, you need to create an iCloud account (using your existing Apple ID if you have one already, or by creating a new one if you donít), and then turn on the iCloud services you want to use on each of your iOS devices and computers.
The Apple ID email address and password you use to turn on and use iCloud services and to access the web applications at icloud.com.
You can use the same Apple ID that you use with iCloud to access many Apple services, such as the Apple Online Store, the iTunes Store, the App Store, and the Mac App Store. When youíre asked to sign in using your Apple ID, enter the same email address and password you used to turn on iCloud.
It sounds like what you've already tried should fit the instructions in the second quote. Maybe logging in with that Apple ID on the iCloud website will "add" the iCloud information to the Apple ID?
I don't recall having any difficulty when I recently set up iCloud, so I'm not sure what else to suggest. Maybe even changing the password through My Apple ID
would be worth a try.