Blower for heater only runs on high - 2000 Dodge Caravan

you should make a diagnostic to know what happened to your car
of course you need an auto diagnostic tool : http://www.chinasnoy.comand you can find all kinds of tools in chinasinoy.com

try resistor...

The heater blower is normally controlled by voltage sent to the blower via a resistor network.
In this case it seems that this unit also called the fan resistor is defective.
I assume that 4 is the position where the blower is running HIGH and in this position the blower is powered directly without using resistor for lowering the speed of the blower. In step 1 - 3 the blower is powered via the mentioned resistor network.

In my opinion the resistor network is defective.
Replace it !!!!.

You are probably going to need a blower resistor,High blower runs a seperate relay and the other speeds run through a resistor.Ussually located on the heater box under the dash.

bad relay switch

If you mean the fan only runs on high speed, then you need to replace the heater blower resistor. It is usually located on the heater box, close to the blower motor.

replace the blower motor resistor located on the heater box were the blower motor is located the wiring to the blower may go to it. This is very easy to locate if you buy the part first.

If blower only works on high speed I would say blower motor resistor but if it does not work at all I would suspect blower motor. Make sure you are getting power to motor if not it might be blower motor switch.

Either the blower went bad or the heater relay went bad. This does not sound like a heater core problem unless you where smelling a SWEET smell when it was running.

Check or have checked the blower motor resistor. This is usually how they act.