If wiggling the laptop lid reconnects the webcam, you've got a hardware issue. The behavior of it being connected on startup then disconnecting sounds like a thermal expansion issue where electrical contact is lost as the connection heats up.
However, I'd try installing the latest Intel Chipset Device Software with the -overall switch to ensure the update all the drivers before sending it in for Warranty repair.
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT