I agree, it's probably the resistor. It's located underneath and slightly behind the glovebox. The part is about 20-30 dollars. I have a Chrysler Town and Country (2001) which is nearly identical to the Caravan and mine did the same thing...the fan crapped out at around 90,000 miles, only worked on high. I ordered the part online and took me about 20 minutes to fix...well worth it....
I just changed the one in my wife's 2004 Sebring Convertible. Took about an hour (give or take time for a beer). Purchased at local Dodge drealer, he quoted $47, I told him I seen it online for $38 and he immediately dropped price to $38. (eh, yea).
The bottom silencer cover removes with a 16mm socket. Pulls off with a minor amount of difficulticy (must twist it to a small degree to get it to remove).
Next remove the two screws holding assy to heater casing with a 4mm socket. Remove resistor assy and then pry up red clip on side. From other end use small flat screwdriver and pry up latching device on wiring socket. Wiggle out multi-wire connector. (I had to use a small flat screwdriver and pry on each side a small amount until free - very tight).
Next step (at lease in my case) is that the new part is physically larger then the original. I had to enlarge the hole the assy fits in with a Dremel tool and round grinding bit. **Check before enlarging as the assy only goes in one way (it's not symmetrical in shape and only seats in one orientation.)** Ice cold beer helps in this operation.
Once satisified that the new part will now seat, attach connector to new assy and close red metal latch. Insert into hole and reattach with screws again using 4mm socket. Replace silencer panel and lock into place with metal nut using 16mm socket. Run heater fan and test. Pop another beer and see what's on espn.
If resistor assy fails within the next couple of years, need to change blower motor (about $110 for parts and $20 for beer.)