First off, there's a good chance you won't be able to use both the on-board and the video card at the same time. YMMV.
Having said that, try reinstalling the on-board drivers.
The "Intel 82579LM" is actually the integrated Network adapter, and not the video. Your on-board video is the Intel HD 2000.
Download the latest video drivers from either HP, or directly from Intel.
Uninstall the Intel video drivers, disable or remove the video card, reboot into Windows, and let it detect the on-board video again. Give it the driver you downloaded.