Q: ICloud won't relinquish ancient ID...

Hi there. Although my newest iphone shows up under my Apple ID ("you are signed in on these devices") two months in I have still not been able to solve the "ancient, expired I.D" problem with iCloud on this device. Every day icloud requests the password for a long-extinct account (from back in iphone 3 days!! :))

iCloud works fine on my two older phones, but not the new one--and again, the new phone is logged as one of my devices in my Apple and iTunes account.  I have tried to follow Winston's advice about deleting icloud from this device, but (of course) since I can't log IN to iCloud, I can't delete it. I would really appreciate any advice on this--it is kind of making me crazy, especially since I can't back anything up, or download and install Find My Iphone to the new device.

Thanks, all!