Problem is the chinese special, they have conquered the small motor and appliance industry.
Huge hub yet small motor runs so hot but hey it's a fan. Low speed is still medium hurricane because that is how you make a motor using minimum copper. Big enclosure for big effect but with small blades.
I also have a Lasko box fan, it's so damn cheap. Last year the handle broke, this year I went to pick it up and my thumb poked through the thin grille.
Grille is USD $12, handle $5.95 I have to laugh, as if they're repairable.
Seems fake: "
Made in America, our 20-inch box fans from Lasko feature all the technological innovation you expect."
So I have no capacitors- only the three-tap switch and motor. I end up using it with a variac during summer to tone down the hurricane.
OP you might have a shorted switch or motor winding, with no run cap(s) I'd expect it to have little torque and not run at high speed.