Excellent that you have tested different things and it seems to be a driver problem. On this same computer did NCS or any other webcamxp program worked with this camera?
On the other computers where it works is this Quickcam Orbit/Sphere AF installed? I am not so worried about the HP drivers, but this camera driver might be the problem.
What you can do is:
-delete the "USB Camera" driver. Connect the ELP camera again. Wait a little bit so the driver installs and then start webcamxp. If it works, fine.
-if it do not work delete both the driver for QuickCam Orbit and the USB Camera.
-connect the ELP camera again and let it install the driver. Start webcamxp again. Hopefully it works.
You might need to restart the computer after deleting drivers just to be sure the driver is gone.