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Before you worry about it being dead check if it's a power issue first - most smart thermostats have a backup battery that dies or needs replacing, and sometimes the display just goes dark when that happens. Try killing the breaker for 30 seconds and turning it back on, or if theres a battery compartment look for a dead battery in there. If that doesnt work and theres no power light at all, you might need a new one, but honestly nine times out of ten its just a dead backup battery and a quick fix.
Power and battery are definitely the first things to check, but don't skip looking at the wiring behind the faceplate itself - sometimes the display connector just gets loose over time, especially if someone bumped the thermostat or there was vibration in the wall. Pop the faceplate off carefully and reseat the ribbon cable if you see one. Also worth knowing: if it's been a few years and the batteries are dead, replacing them might not wake up the display if the thermostat hit some kind of low-power shutdown mode - in that case you may need to do a full reset by cutting power at the breaker for 30 seconds, then restoring it.
Had this happen to my Nest a couple years back where the screen just went black midway through the day. Turned out the C-wire connection at the back of the unit had worked itself loose - pulled the faceplate off, reseated the connector firmly, and it came right back to life. Worth spending two minutes poking around in there before you assume the whole thing's toast, especially if the thermostat still seems to be working (heating or cooling is running normally). If that doesn't do it, then yeah, battery or a deeper hardware fault, but that connector thing is surprisingly common and super easy to fix.
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