iCloud assumes old Hotmail account which doesn't exist and has a forgotten password

Good evening. I'm trying to log into iCloud on my iPhone, but the default account it has is an email address I no longer use, no longer exists, and I don't remember the password. I have a new, functioning email and password and an apple id which works fine for purchases in the iTunes store, etc. For some reason when I try to log into the iCloud function on my iPhone, it asks me to enter the password for a hotmail account which no longer exists, but used to be my primary email for apple id about six years ago. I tried looking up apple ids using the Find your Apple ID function, but it only sent me to my current email and tried to get me to reset my password. Is there anyway to reset the primary email account or switch from an old iCloud account to my current one without the old password? I even tried to add another iCloud account and then delete the old one, but when I tried to add one with my new email address and clicked enter it said that account already existed (though when it said that account, it referenced my old email address instead of my new one, so obviously the new are already connected).