Why my baseboard heater won’t turn with new thermostat?
The only thing that comes to my mind would be a possible wiring issue. If the old stat works properly that can only lead to one thing. Improper wiring on new stat, or a bad stat right out of the box. Believe me when I say this, its more common than one would think. 
 I would double check the wiring. Double check the programming. If all that checks to be normal and within the manufacturers specs. Then that would leave one to reasonably believe the stat is bad OR incompatible with your system. I know this isn't a lot of help to you. 
 I have seen many cases where components and parts have been DOA right out of the box.