It sounds like you've checked things related to it's failure already but I'm still wondering about corrosion or oxidation on the battery terminals inside it. Anything that could break the battery power from reaching the circuitry. This kind of failure isn't heard of on here. I'm also guessing you're 'booting' the system in the correct order when you changed the rain gauge batteries, 1st the rain gauge batteries insertion then 2nd, the thermo/hygro and wait a couple of minutes for signal acquisition from the rain gauge then 3rd, battery removal/replacement (or reset) on the console display lastly?