Old iCloud ID stuck on iPhone, forgot password, I can't change or delete account

Here's my situation:

I have an iPhone 4S

The iCloud account on the phone is an old Apple ID

I don't know the password

The email is no longer supported or reachable

I must have entered the wrong birthdate because I can't access the security questions

I can't delete the iCloud account fro the phone because Find iPhone is ON

Find iPhone can't be turned off w/o the password to the old iCloud ID

I have a current Apple ID that is set up to all other aspects of my Computer and iPhone

The iCloud on my computer is under the new ID

How can I remove the old iCloud from my phone and change to the new one?