In that case you should be safe. Any modern system will have at least one PCI slot. One way to find out about your video card, at least in Windows 98 or newer is to open the display control panel and then choose advacned. There should be an adapter tab in there and it will list it. I don;t recommend you doing much fidgiting about, as it seems you are not well versed in Windows Hardware info.. but at the least it can identify your video chipset...
Also check the HP website for the Computer model and it will list all that stuff as well..
Did the research on your model and I think I see your problem.
Yes you have integrated video. The owners manual should tell you how to disable it. I really recommend having your buddies give you a hand, changing video drivers is actually the tricky part.. installing the card itself is easy to do.
Here's what HP says you have on your system:
Attribute
Properties
PCI Local Bus Controller
Intel 810
Video Memory
11 MB shared memory, Integrated graphics, not upgradeable
Feature connector
(game/joystick)
Yes
Resolutions (video resolutions dependent upon specific display used)