replacing the nutone doorbell button/box with a regular button

We recently purchased a home that has a nutone doorbell system. The house (built in 1975) was originally wired with intercoms in every room, but the people we purchased the house from (2nd owners) removed them; however, the doorbell is still original, including the outside doorbell buttons/boxes. I tried to replace one of the boxes with a regular doorbell button that I purchased from a 'big box' store, and quickly realized that was probably not the right way to go. When I took the box off of the wall, I saw that there were a few extra wires attached to the speaker. I tried to ignore them, and just attach the red and white wire to the new button thinking it would work, but when I turned the power back on the doorbell didn't work...was I supposed to do something with those extra wires? Am I supposed to only use a nutone button? Do I have to replace the whole doorbell system? I'd prefer not to have to do that, because there are two entrances to the house, and I like the fact that there are two different tones for the two different doors, which is very convenient. Any advice??? Thanks!

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