it is not grounded.

Mains voltage motor, metal casing, metal drill press, metal everywhere, and not grounded? Sounds a bit dodgy.
Anyway, I'm gonna totally and uneducatedly guess capacitive coupling through the case and you to earth. Plugged in one way the Active (Live, Phase) is connected all the way through the motor to the switch - all that forms one side of the capacitor, the casing, you and earth forms the other.
Plugged in the other way it is stopped right at the switch and it's Neutral which is running all the way through the motor, no capacitance since it's (roughly) same potential both sides.
Turn on the switch and you wind up somewhere in the middle.
There is no power behind the coupling, enough to feel that hum/vibration/tingle, but not enough to actually pass current.