This is your products right?http://h10025.www1.hp.com/ewfrf/wc/product?cc=us&lc=en&dlc=en&product=3436818
You don't have any Graphics card, but you may have the IGP (integrated graphic) broken. You've the possibility to put a new card though. If you would, you can try putting a graphic card in your PC and see if it works. If it does then you should put a card there because the IGP is broken. If it doesn't work then something else is broken.