Power supply for toothbrush motor
If this motor runs when directly connected to a 1.5 V battery, then it will run when connected to any other 1.5 V source.

The reason it doesn't run with your other power supplies is probably because the motor demands more current than the supplies can supply, and they shut down or reduce their voltage.

Note that motors take more current when starting than when running.  Your supplies might be rated for the running current, but never get there because they shut down or collapse due to the starting current demand.

You can easily verify this.  Put a voltmeter across the supply and see what happens when you connect the motor.  You will see the voltmeter go to 0.

The solution is to get a supply that can handle the current requirements.  If a AA battery works, then a couple of amps should be good enough.  With a benchtop supply, you can set it to 1.5 V, then adjust the current limit to see what it takes to allow the motor to get going.

Another thing to try is to connect a large capacitor across one of your existing supplies before you connect the motor.  If the capacitor is large enough, it can source the initial current to get the motor going, then the supply can catch up and source the current to keep the motor running.  At this low voltage, you can get sufficiently large caps.  I'd try something like 10 mF or more rated for 10 V.