iPhone Access bug

Hello.

I have my iPhone 5c 16GB and today it has run out of battery. I wanted to turn it on but it showed me the white "welcome to iphone" screen. I was surprised that the iPhone has completley restarted but then when I choosed my wi-fi network the iphone asked me to write down the Apple ID and Password. The apple id is in this format - m*****@a*****.sk. I could tell by this that this was my first email adress which I was using in 2014 but I already switched to new a long time ago. The iCloud and everything was logged to my new Gmail adress. The iphone is now asking me for a old adress and I forgot the password so I wanted to recover it but it says that my email m*****@a*****.sk doesnt exist and it is not a valid APPLE ID. This surprised me because the exactly same email as Apple ID is asking me to fill up in the iPhone welcome screen. Im so confused now, i tried to recover my apple ID by the iforgot apple site but every times it shows "No apple ID found". Im on my old mail right now and I have proof that I changed mail to new gmail, they sended me mail back in 2014 and I can even log to my new gmail iCloud and track the iphone and see the things on my iphone. Im very confused and asking you for the help. What should I do? It looks like the iPhone is stuck to my very old email adress. I was using the new one 2 years with no problems, with iCloud and iTunes and everything was fine on the new adress