The lens on a compact camera is the major moving assembly and faults/damage can occur.
My lens is failing
Lens error displayed on the rear LCD
If you turn the camera on, it powers up, the lens comes out then retract straight away
Impact damage - lens slightly bent
Lens jammed out
Will not power up
Lens making a grinding noise
Sand in the lens assembly
Why has my camera lens failed?
There are many reasons why a lens fails.
A mechanical failure in the lens assembly
The auto focus gears may have jammed or broken
The camera has sustained impact damage
Sand has penetrated the lens assembly – this will jam the lens gears
The camera has been accidentally turned on while it is still in the camera case
Can this be repaired?
There are generally two different repair processes for a lens repair 
Dismantle the lens and re-seat the lens assembly
Dismantle the lens and replace the complete lens assembly - the complete assembly can be costly
Note:  The auto focus motor in a compact will produce a slight noise, this is because the auto focus in a compact is always working.
The noise you hear from the auto focus motor is normal. In some cameras the auto focus noise may be recorded in movie mode.