It may be possible, but probably not. I would only attempt this if I was about to get a new laptop and upgrading this one would be a bonus or a reason to go ahead and buy a new one.
First are you able to remove the card see if you can. Taking a laptop apart is tedious and a pain lots of small screws and plastic parts that break easily.
Does the card look like this?http://www.ebay.com/itm/HP-NX9420-NW9440-256-MB-ATI-Radeon-X1600-Video-card-409979-001-/370556165486?pt=PCC_Video_TV_Cards&hash=item5646de5d6e
If you take it apart and the video card looks like the one I linked too then you might be able to upgrade it. but even if your does come out and a different one will fit in it still amy not work.