Firmware Locked Password
Firmware passwords are a security measure intended to stop a stolen Mac from being used. Quite correctly, in my view, Apple won't help you unless you have a receipt or some other way of establishing ownership.
Have a read of this from Topher Kessler which talks about how the firmware protection is implemented and the steps needed to erase the firmware password.
If you do find a way to bypass the firmware password, you probably should not publish it here.