New doorbell stopped working, now not working properly

I have a doorbell question. Here is my setup. Years ago I added a wireless electronic doorchime "extender" to our existing wired doorbell so that we could hear the doorbell in our basement. All worked well. Recently, I replaced our doorbell with a brand new Honeywell wired doorbell, including the button. We have no back door doorbell. The only thing I didn't change was the transformer because it is wired directly to our electrical panel, and I'd prefer not to mess with that. The old transformer is a 10V 6VA transformer, while the transformer for the new bell (uninstalled) is a 16V 10VA transformer. The doorbell has been working fine for over a month, even with the old transformer. However, we woke up one morning to the chime in the basement ringing non-stop and the new doorbell quietly buzzing non-stop. The light on the doorbell button is not working, so I replaced the button. The new button is lit, but now the doorbell "dings" once, but no "dong". What can the problem be? The transformer? If so, why did it work well for all this time? I'd appreciate some help. Thank-you.