I measured the base current with a multimeter, I measured 430 milliamps base current. And the tip110 transistor will still spin the motor without the arm or any load.Calculate the base current:

1) Base voltage for a TiP110 is typically 1.8V on its datasheet.

2) The 4.2V battery is almost dead at 3.8V.

3) You have a 1 ohm resistor limiting the base current.

4) Then the base current is (3.8V - 1.8V)/1 ohm= 2A.

5) If the battery is working then you destroyed the base of the TIP110 because its maximum allowed base current is only 50mA.

For a load of 2A then the base current is shown to be usually 2000mA/250= 8mA, then the base resistor is (4.2V - 1.8V)/8mA= 300 ohms.

The saturation voltage loss is 1V to 2.5V so the motor gets 3.2V to 1.7V when the battery is fully charged at 4.2V.