Chevy’s are horrible about burning up blower motor resistors and the wiring going to them. Find it and check it out. It would not surprise me at all if you found melted and scorched wires and plastic. Although, I’m not sure there is a wire there that is battery power- I would expect only ignition power. So you may have a relay burned up too.
in my wife’s ‘12 malibu, the resistor is up where the floor meets the under dash- right where my 6’ son likes to put his feet… (not sure if your '05 Impala is located in the same place.)