My pc has a dual core 2,53 gHz Intel celeron processor with 1 gb of DDR2 ram. I have the available PCI slot. I'm not a gamer. I'm interested in getting my PC to run a dual monitor configuration and running DVD video as smoothly as possible.
Like Factor Mystic says, but to answer your question of how to recognize this:
Those are both PCI-Express cards, so as long as your motherboard supports PCI-E (It's a different sized slot) you'd probably be okay.
If you are looking into the 9800 Nvidea cards keep power in mind. Those cards need their own power source from PSU. Usually 450 watts and above.
The short answer is PROBABLY not. Since it is "crappy" it is probable several years old, the power supply will not have the required connectors, and the MB will most likely not have PCI Express. Probably AGP and PCI only. but check the pix above, you might be lucky.