My bad you have a resistor. The automatic system has the module.
It is possible for the resistor to not allow the fan to work at any speed. It has a fuse built into it and its the first thing the ground side of the blower runs into.
The dark blue wire should have power to it all the time with the key in the run position. The black wire is the power going to the blower. The green wire is the ground side of the blower. You can check continuity between the pin on the resistor that the green wire goes to and the pin on the resistor that the blu w/gray tracer goes to. This would be the path that the high speed uses. If there is no continuity than that is a problem since the thermal fuse is in between these two pins.