Originally Posted by hybrid
Here's what I think I know about the problem. Yes, there is a relay that feeds the blower circuit and that relay is found next to the flasher relay under the dash. But there is also a blower resistor (Part number 4L3Z 19A706-AA) used on 1997 through 2004 F-150's that controls the low speed operation. There seem to be two other things to look at if just replacing the resistor does not fix the problem: The switch itself may be bad, but it is usually a problem with the switch connector contacts. You can buy a replacement pigtail to repair the harness.
The resistors are placed in the air flow so they are cooled during blower operation. If the blower does not run because the blower motor is bad or disconnected, the resistor usually overheats and fails. GM vehicles use a similar system, but many use a printed circuit type resistor rather than a wire coil. I replaced one of those yesterday in a car where it looked like a box of tissues was placed on the floor near the recirculating inlet and the fan sucked a couple into the system. The tissues plastered themselves to the inside of the squirrel cage and blocked enough air flow to burn out the resistor. Note to wives: No Kleenex boxes near the A/C suitcase.