There should be no direct relation between cooling system work and the blower motor working. This sounds like a set of worn out brushes in the motor. If you can find them in your area they can be replaced. If you check on the top of the firewall to the right of the brake booster can you will see a connector with three wires. The red is system voltage 12 or so, the yellow is the control voltage signal for the blower regulator. It varies depending on the speed setting on the ACC panel, but it should be between 2.5 and 7.5 volts or so (don't remember the exact numbers) The black is ground. Get a voltmeter, unplug the connector and check those voltages (with the key on and either high or low speed selected, or, better yet, select defrost.) If they are OK, then it's the motor, if not, then it's in the ACC module. If your blower is squealing, growling or the like, it is probably the brushes..
2000 Dodge Grand Caravan SE
No matter what you fix, there will always be something else to fix..
"Warranty" is just another way of postponing the inevitable.