Customer support issues

Hi there,

I purchased a brand new iphone 5C in lime green from an Ebay business seller. The phone was listed as brand new and sealed. After 3 months the phone stopped being able to make/receive calls. I had no joy with the Ebay seller so spoke with Apple who informed me that the serial number was for an iPhone 5S in gold (not my phone). Furthermore they told me my serial number was for a product that had been replaced. Also there is no serial number on the sim tray.

I submitted a claim via paypal as the phone I purchased was not the phone they had listed and they say I have to provide proof. Now my problem is that whilst Apple will verbally give me the information over the phone they will not email it too me due to privacy rules due to the serial number of my phone belonging to a replacement phone or not a genuine phone! Where do I go from here?