Ceiling heat or cable heat is or used to be quite common in the Pacific Northwest.
It is a resistive wire that gets warm when power is applied.
If the heat works with the thermostat turned up the resistance wire is good (it works or it doesn't).
I would consider having an electrician connect the thermostat if you have tried and failed but the original thermostats were Bi metallic springs connected to contacts (a simple open closed switch). More recent thermostats are digital and they have to be connected properly to function.
Ceiling heat is not something that works well unless being used all the time. It takes time for the heat to penetrate the ceiling and warm the space.
Changes in temperature can take several hours to equalize in a room.
I have been called when folks new to cable heat or ceiling heat thought it was not working and tried to replace the thermostat with one not rated for line voltage (lucky they could not hook the #12 wires in that case to the 18 awg connections).
But depending on the spacing it may take 3 hours for the room to come to heat. The other rooms may have more cables thus heat faster.