Ding, dong, the doorbell is still dead

I was quite proud of myself today...which quickly evaporated. I was on my way to HD to buy a new transformer for our broken doorbell, thinking that was its problem. As I stood on the stepladder with my flashlight in the basement, I learned that the voltage for the existing transformer was only 8 volts. I think I had assumed it was more like 12-15 so I really thought it was kaput. Seeing that and testing it again, it was exactly 8 volts. So, the transformer is fine. So I figured we just needed a new button. I went to HD and got a nice one and returned home to install it. Unfortunately, despite its beauty, it still doesn't work. So, no issues with transformer, button is new and properly wired (I am pretty sure, at least), so that means it's either the chime or the 90-year-old wiring. I am thinking that instead of buying a new chime or having to rewire, I'm just going to buy a wireless one. I know, I know - tacky, but functional, right? Maybe I can find a cool-looking one?