Is the MOSFET NTE2390 broken if connecting only source and drain powers a motor?
I've got a small motor wired to the drain of an NTE2390

the other end of the motor hooked up to ground.

the source of the MOSFET to power



That MOSFET is an N-channel device and its body diode will freely conduct current from a positive supply to a load when incorrectly wired into a circuit: -

You are using it incorrectly. If you want to connect source to positive and load to drain (returning current to ground) then use a P-channel MOSFET.