If you swapped the suspect 2-wire non-programmable with the known good 2-wire programmable from the bathroom and it works properly, there is no other conclusion. The 2-wire non-programmable is broken.
Technology Editor Bill Wong didn’t have to pull a new cable to fix his thermostat. He should have tried Energate’s EZWire instead. In an earlier post, I described how a snafu with my Nest thermostat ...