I have an Elitebook 6930p with a docking station that has VGA and DVI out on it. I currently have LCD monitors hooked to both of those ports and everything is working as expected. Is it possible to get the laptop monitor to work as well with those other 2 monitors giving me 3 working displays?
From my experience very, very few laptops are capable of driving more than two screens at a time, most laptops will let you use any two of the 3 available screens/ports, but no more.
The only time I've ever seen it is on a gaming-specific laptop that had 2 GPUs (essentially 2 video cards) installed.
Looking on the HP website, I can't find a manual for your model, the closest to your request is this page http://h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?cc=UK&lang=en&objectID=c01369231&prodSeriesId=3688868&prodTypeId=321957 that definitely only ever mentions two displays at a time.
The only other option for a 3rd display is to get something like a USB screen, or a USB display adaptor. Something like the options in this question http://superuser.com/questions/112887/can-i-use-a-usb-monitor-like-mimo-as-a-primary-monitor or this one http://superuser.com/questions/127743/can-anyone-recommend-a-usb-to-dvi-adaptor-which-runs-well-under-windows-7