Hello omk,
If you are still facing the problem,
tilting the drone, in which case only the motor that is at the lower end of the tilt rotates. The weirdest part is that this behavior is only when there are propellers on the motors. Am I missing something?
This is the expected behavior. If all the motors rotate properly when controlled from LibrePilot software, motors may be probably fine.
Try:
Remove all the propellers, give a small amount of throttle only(no roll, pitch or yaw) from transmitter, tilt down a particular motor arm, check if the dipped motor rotates. The motor which is dipped more than the others must gain speed continuously. If not, check the motor numbering as per LibrePilot and as per the flight controller. Throttle down and repeat this for all the 4 motors to verify.
Regards,
Raj Gunaseelan James