Thanks everyone for your help. I tried to attach this reply to my
original post, but for some reason it is not working.

I was able to solve my door bell button problem by researching online.
It ends up that I have a door bell that one can select different chimes.
In order for it to work, a small wire with a diode on it must be put on
the new door bell button, and wrapped around the two screws. I did wonder
why my new button did not have this wire on it.

It took me three minutes to fix the problem, and two hours of wasted time
trying to figure it out. Oh well, I learned something new, and
saved some money.


*I recently found out about the needed diode when one of my customers
purchased a new LED doorbell button and found that her doorbell would not
work with it. The instructions for the button barely mentioned the diode
and didn't say how it could be obtained as it did not come with one. She
decided to look for an old fashion neon button instead.