I have an older 100,000 BTU Carrier downdraft gas furnace that has an electrostatic air cleaner on it. I cleaned the filters on it for the first time in several months and replaced them when dried. Now my blower immediately kicks on (after I turn on the furnace switch) and runs constant and the pilot light never does anything. Any suggestions?

Did you by mistake hit a fan switch? Check your thermostat and see if the fan switch is set to "on " or "Auto". Set it to "auto". Look on the cabinet of the air cleaner to see if there is a fan switch on that as well.

No, I have gone so far as to even turn the thermostat to the off position and the blower continues to run. The air cleaner cabinet has a power and test button, and I have tried it with the power off there as well.

Something has crossed the R and G terminals in the furnace to short them out. Check all wiring near the furnace and air filter cabinet. Try removing the wire from the G terminal in the furnace cabinet to see if the blower stops.