A servo that buzzes or hums without turning is the usual symptom, and it almost always means the servo is being told to move but cannot. Work through these in order.
Power. A buzzing servo is most often an underfed one. The Rover runs on six AA cells. Fit a fresh set — all six at once, same brand, and alkaline rather than rechargeable, because rechargeables give 1.2 V instead of 1.5 V and the servos need the extra headroom. See "Can I use rechargeable batteries in my DIY kit?". Several servos pulling at the same time need more current than a part-used set can deliver, so cells that still run the screen can easily be too tired to turn a servo.
Connectors. Unplug and reseat every servo and motor connector. Check each one is pushed fully home and the right way round, against the build guide photos. A connector that is one pin out, or half-seated, gives exactly this behaviour.
Mechanical binding. Take the servo horn off and see whether the servo turns freely on its own. If it does, something in the linkage is jammed or over-tightened. Check the horn is not fouling, and that no screw has been done up so hard that it binds the joint.
Firmware. Connect the Rover to a computer, open code.circuitmess.com and use Restore firmware to put it back to its factory state. That rules out a half-finished upload.
If it still will not move, email [email protected] with:
A short video with the sound on, so we can hear whether it is buzzing
A photo of the board showing the servo connectors
Your order number, and which servo or motor it is
The video is the useful part. A buzz, a click and silence are three different faults and we cannot tell them apart from a description.