I need help replacing this doorbell...?

I have a doorbell that uses 4 C batteries yet has wiring coming in from the two buttons. This unit stopped working recently, and had a buzzing noise coming from it with hot batteries. I removed the hot batteries for safety however fresh batteries did not fix the problem. I'm fine with buying a new unit but I just couldn't find or hear of a new doorbell unit with batteries and wired chimes. The new ones are all wireless buttons with battery powered chime unit, which sound fine but they all come with very cheap and ugly looking buttons. Has anyone ever seen this before? Then, can I possibly be provided information on a unit that can replace this one by using the existing wiring and buttons that also take batteries?