Since I can no longer purchase a Honeywell T8401C100 like the one that came with my mobile home, what is a good Honeywell thermostat to use to replace it (the buttons on the original are unresponsive)? My guess is that it would be a Honeywell RTH111B1016, but I am not certain.

Before we try to answer I need to know what type of furnace or boiler you have and the type of fuel. How many wires come out of the wall to the stat

Here's Honeywell's suggestion: https://customer.honeywell.com/en-US/Pages/ProductReplacements.aspx?pid=T8401C1007/U