A lot of this is speculation. I'm too big a coward to experiment and possibly separate my own iCloud and iTunes accounts; so take it for what it is worth.
Your iTunes account and iCloud account are two separate things. Or at least they can be. Depending on how you have things set up, changing the Apple ID (email address) or password in iTunes may have no affect the iCloud account (though yes, they can be the same email and password and when you create the iCloud account it will by default use your iTunes info).
I am not certain of this, but I suspect that you can not change the iCloud email address itself; because iCloud is an email service (among other things). That address, just like a Google email or Yahoo email, is the accounts primary identification.. I'm not sure what will happen if you change the email address of an account where the iTunes and iCloud account are the same. They may split, for all I know.
Your iTunes account by contrast is just a way for you to buy stuff. It isn't necessary for it to have a immutable online address.
So, try the old info for signing onto iCloud. It will probably work. If you want a new password, you will need to change it for iCloud itself, not in the iTunes account settings.
Apple IDs and iCloud
iCloud: View or change your iCloud account information
https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/