Today a small camera board made by Sanm arrived in the mail from Hong Kong. It came without a USB cable, just a 5-pin header, so I used the pinout diagram on its product page and wikipedia's USB pinout reference to put together a cable.
Sanm pinout: 1 VDD 2 D- 3 D+ 4 GND
Then I took out the filter by unscrewing the lens and prying it loose, closed it up, and plugged it in, and it worked. It identified itself to my computer as a "BisonCam NB Pro" which appears to be the internal webcam of the MSI GT780R.
In order to get a flat surface for mounting, I used the broken off mounting point of a Syba cam, and stuck the Sanm board to the side of it with double sided tape. In this photo I marked where the body of the Syba cam had been with a pen, and ticked off the lens location, for comparison. I believe my lens placement for the Sanm camera is roughly the same place as the Syba cam:
the results are a little dim, despite the otherwise great quality of the camera. Any thoughts?