I have a chinese RC car . I replaced the battery with a 5000mah power bank so that it can last more. The problem is using the remote control, the steering is turning left and right but the car itself is not moving because the rear motor is not working.

When I give direct DC 3.0V to motor, it is running ...but not with the its power supply. What could be the problem? Any ideas?

check output of your powerbank or try with high volt battery.

i think you are using a toygrade HB mousepotato clone. If your one motor is working fine, then there is no isue with the power. You should remove the casing and check the wire connection. There is a chance of loose contact. If everything is good open axle casing and check your motor terminals using a multimeter while applying throttle. If you could find enough voltage your motor is done. You should replace the motor. But the problem is you should replace both front and rear motors. Else the RPM of both motor will be different. If you couldnt find enough voltage in motor terminals replace your wiring and check the motor later