Blower motor resistor

Probably ought to check out the blower motor RELAY first... https://www.autogenius.info/lincoln-ls-2000-2006-fuse-box-diagram/

You don't have a blower motor resistor. Your car uses a blower motor controller. A little fancier than a pack of resistors. It uses a transistor to pulse the blower motor on and off to get different speeds. It sounds like the transistor has failed HIGH or ON giving the blower motor full ground meaning the blower runs at full speed continuously. It will be located right next to the blower motor itself which is usually located above the front passengers feet.The transistor has a large heat sink inside the air duct system to cool it off with the air from the blower. I personally would use an AIRTEX/WELLS one from rockauto, but without testing to confirm first, that would be an expensive guess($139). You can google or look on YouTube on how to test it if you want to.