The first model comes with 7 speed but I can only see only 5 TRIACs on the board.
Not sure how it works.
Meanwhile the second model comes with 3 speed and 3 TRIACs available on the board. I assume 1 TRIAC for 1 speed.
While troubleshooting they look like their µC don't have enough power to start. The buzzer give something like repeating click sound. I did measure the µC Vdd/Vss and found out that the voltage is less than 5V.
After a quick search at Google, lead me to aztronics . Similar symptom. So I give them a try.
Desolder the capacitor and measure. Binggo! All caps (regulator part) value is less than they should be.
Replace them all and test with a smaller vent fan.
Done and pass them back to their owner to test with the their ceiling fan motor.