Actually, from the old
GFX card, it sounds like the pc actually has AGP, if this is infact true, then it will be possible to purchase an AGP 3850, once it is available, although their availability will probably be questionable once it is finally launched.
In the meantime, to check whether it is infact AGP or PCI that your
GFX card is running on, you would probably be best of taking a picture of the connector that connects your
GFX card to the motherboard, then posting it on here, that way we will be able to tell for sure which type of connection it uses.
I am 90% sure that it will have AGP, as i have not seen a midrange P4, as your would have been in its time without it. I especially doubt that they would have made one without AGP in 2004.