I re read your posts and you never said if the furnace blower started or not......so assuming not, then checking power at the thermostat is the easiest. Open the case of your new wall thermostat and place your voltmeter from R terminal (+12v) to B terminal (Gnd) as Beau388 said. The thermostat terminals should be labelled. If you see the 12volts then the switch is on in the furnace and voltage is present there too, because the furnace provides power to the thermostat typically. It does not mean the furnace does not have a problem though. If no 12volts at the thermostat then you have to go to the furnace wiring and find out why not or check for open fuses or breakers. Some thermostats also have a small in line fuse inside them or in the wall feeding them; make sure that fuse is also good if you can find it.
You should hear a small click at the thermostat if its small internal relay (call for heat) is working (powered by the 12vdc and a call for heat at the thermostat). The hardest part sometimes is figuring out how to remove the thermostat face plate without breaking any plastic parts. I am attaching my thermostat conversion picture to assist you.....look at the left side which is a “typical” analog thermostat wiring strip. Also since you changed your thermostat make sure your wiring is correct.
I am also including a generic schematic showing a basic connection of battery, furnace, air conditioner and thermostat to provide an overall generic view.
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