The only idea I have to add to that would be to check the brushes in the motor, if they are of the serviceable / replaceable sort (but probably not, from what I can see in the photo). The motor might simply be dead, but there isn't really much to fail in a simple DC motor unless it's been burnt out through abuse (run on the wrong voltage, or overheated by being overloaded or stalled).
So I'm wondering again about the wiring - everything suggests that it is a simple two-wire hook up, but it might be something different. We'd need a better photo of the end of the motor to determine that. The only other alternative - assuming the motor isn't dead - is that the 'internal' limit switches are cutting off the power, but that presumably shouldn't be the case when the ballscrew mechanism clearly isn't at either end of it's travel.
Jeremy