for power to get to your blower in normal operating conditions it must go through the ignition switch, hopefully your ign switch is bad otherwise you have a power wire melted to another power wire leading to your ignition , blower or accessory wires. get a wire schematic and see if power to the accessory's turns of with the key like it should.
You have a shorted blower control module. These are located under the hood, sometimes under some plastic covers. There is quite a few different wires going to it, but the one you are looking for will have thick red wires and a thick purple wire to it. The reds are hot battery and the purple is to the blower motor. To be sure just unplug the connector and see if the blower quits. If it does, replace the module. These are pretty easy to change with just two or three small screws to remove. Good luck.