How can I test a dc motor?
Measure the resistance between the motor terminals and compare it with a known good motor (or the datasheet). If the coils have melted, they will have shorted and you'll see a lower resistance. Or they will have broken altogether, and you'll read infinite resistance.

Turn the axle of the motor with your fingers and compare it to a known good motor. A bad motor can sometimes stick, or feel like it's got a lot of friction.

Finally, connect a known good motor to a variable voltage power supply. Turn the voltage up slowly from zero, up to the motor's rated voltage. See how the motor behaves.  Do the same for the suspect motor. Compare them.