Can I upgrade my computer video card from the 82945G Express Chipset Family?

I've got a cheap Dell computer that has an integrated graphics board. It's the 82945G Express Chipset Family. It is pretty wimpy when it comes to running games. As luck would have it, there are many games that do run well that my children play. However some of the more serious games (like Bioshock) will not run. What's the best way to upgrade this computer? I do not have a PCI-Express or AGP slot. ONLY PCI is available. Is it feasible? Recommendations?