No access to old iCloud account on my brand new phone

All I ever want to do is switch to my new phone that was just delivered... My phone came with a sim card in it so I backed up my old phone and began the process with the new one. The new one said "No Service" so i tried to contact At&t and no luck. I tried to reset the new phone again because it had my settings on it but nothing was working. There is an old iCloud account signed on and I don't have access to the email to verify anything (which is required now). Please help me get this old iCloud account off of my phone so I can restart it.. I am about to lose my mind with this because it happen every time. Never an easy swap.