Hard to answer as not a clue what system you have, but the Y plan system hot water is the default position so it is reasonable common for the three port valve to cause that fault, often the micro switches inside the head, on the side of the valve there is a lever to assist bleeding, moving this lever and latching it open may get the central heating working on a temp basis if this is the fault.
I have a Horstmann DRT2 in front of me, quite a nice programmable thermostat in its day, now used as a thermometer it did not show the battery depleted sign until after it had stopped working, now around 20 years old, the Horstmann HRFS1 we had, gradually lost its connection with the base, not even batteries in that case, just drifting RF frequency, the Flomasta 22199SX replaced the DRT2 with near enough same functions, the Honeywell Y6630D replaced the HRFS1 it was not programmable, but failed safe, battery lasted for ages, and was clearly good quality, which was reflected by the price.
So this house did not want some thing which needed batteries replacing, it does have batteries but rechargeable and charged all the time power is on, I fitted Hive Gen 3. OK swapping the DRT2 batteries every November never had a problem, the batteries would last about 2 years, so change once a year and no problem. But even though the wall thermostat is mains powered, the 9 TRV heads still have batteries, again last around 2 years so change every year not a problem, and they should fail open, but as yet not had a set become discharged.