This am we I got up the blower on my carrier series 100 gas furnace (approx 10 years old)was running and blowing out cold air. Even with the thermostat turned to off the blower runs constantly. The only way to stop the blower from running is to turn the switch on the side of the furnace to off or remove the lower cover/door. What is the possible solution to this problem? Thanks

Bad relay. Sometimes (with power shut off) you can top on it with a screwdriver handle and unstick it. It will need to be replaced though

It can also be a tripped limit. Is it a downflow? Does the heat come on?

Carriers will run fan after multiple retries. Check limit switches and pressure switch.

It could be a stuck relay, but if the heat doesn't come on, more likely it is getting a false high temperature reading. Try to locate the temperature sensor or limit switch. If the furnace has a wiring diagram, it will help if you can figure it out. It could also be a logic fault on the control board. If the diagram shows it as a switch, you can check to see if it is closed. If it is a thermister, there is little checking it. You might just try replacing it.

Some Carrier furnaces will act the way you described if the transformer is burned out. The fan will come on and run but nothing else will operate. If you have a voltage meter check for 24 volts of voltage between Sec 1 and Sec 2 on the circuit board. While checking make sure that the door switch is depressed.

If the blower runs all the time and the heat will not come on or even try to come on it may just be a tripped limit switch. Roll out or vent limit switch. Turn power off to furnace and then back on. If the blower is still running and the heat is not trying to come on, it's a limit.
Good luck.

Just a note on Carrier/Bryant furnaces. If you energize the furnace when the thermostat is calling for heat the blower will run aprox' 90 seconds before it starts its heat cycle.