All I did was take the filter cover off the furnace and changed the filetr to a new one. Now the heater won't come on once I turned back on the system from the thermostat. The furnace is made by Carrier. Did I do something wrong?

FFelix

Look for a possible safety switch that needs depressed where the filter goes/lid. The furnace may be set up not to run without a filter in it and the new filter may not be sensed there. Is your thermostats digital and it needs "reset" pushed because of the "Filter code blinking?

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There is a furnace interlock switch that the blower door depresses when the door is installed properly. The switch could have gone bad OR the door is not installed properly.