I also agree that it should work. But I wouldn't expect much. You have a v1 pcie x16. I'm pretty sure that's a v2 pcie.
This is beside your question. And I don't know what you are planning to do with it. But that system is old old. 1gb of ram isnt going to get you anywhere. If it's something you need to use for anything relevant, I would think the cheapest pc you can find will be better. You could probably find better just by posting on craigslist asking if anyone has something they want to get rid of for free. I'm not trying to sound like a jerk. Just if the card is something you're buying, it's probably not going to get you far.