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look under the passenger side of the dash under the glove box at your blower motor. you will be looking for so melted/ corroded wires on the plug that goes to your blower motor. i had the same problem with my 2003 and it is a dealer part for the replacement plug. they told me it is a common problem.
It can also be because of a bad blower motor resistor pack. That is a very common problem on Dakota's. Use the search terms "blower motor resistor" in the search box here and you will find a lot of posts on it.
Yes do what sl2racer said, My resistor had melted, and I had to replace it. I think I paid like $12 from Autozone, don't really remeber. I had to get a new resistor, and wire harnest tho. Wire harnest costed me $90