Is there a troubleshooting tip for a whole house fan that runs on high speed but not on low speed?

It's possible the low speed winding is not working correctly.

Consult the instruction sheet from the website to assist in replacing the motor with the correct belt tension and wiring. Test the direction of the motor prior to installation to ensure it is correct. If it is not correct, remove the small cover plate on the front of the motor and reverse the blue and purple leads with a pair of needle nose pliers.