What is the exact system model? What is the current OS installed on the system? Is there any damage on the system? When did the issue start? Does an external webcam work fine? Are you able to use the inbuilt microphone? Are there any missing drivers / unknown devices in device manager? What application are you using for the webcam?
Swivel the LCD back and forth and check if the webcam comes on.
Update the BIOS - http://dell.to/1n3X2po - enter the service tag and download the BIOS, update and restart the machine and check.