If you can hear the motor running when you hit the button, then I don't think you will need to replace the motor. If you do need to replace it, I would un-solder it and take it to a hobby store. They sell the same little electric motors for around $5.

The problem with mine was that the motor housing lost two little tabs on the bottom that hold the motor in place (it is just pot metal and they sheared off). I used JB Weld (epoxy) to glue the motor back down to the housing. There isn't much surface area to glue, so you have to use something strong.