Do thermastat Go bad?

How can you tell if your thermstat is going bad. My heating unit is runing fine from what i can see the house is good for hot water. But my heat unit is not trun on the the part of the unit that make the water pips hot for the house. the Thermstat batter where weak almost dead for the most part. so change them with some not so new batter but strong then what i had in there. not sure what to do other the new batter