Short answer, it may.
Long answer this system does not seem worth the upgrade. You don't even have a pcie slot. This GPU is a PCI model, correct? In my experience (tried one last year) they underperform compared to their PCIE counterparts and don't perform well (if at all). If your system was at least DDR3 RAM I would say try the upgrade and at least you can move your new RAM to your next computer if it doesn't do the trick. But DDR2 is outdated and expensive (just bought some myself and kind of regretting it). Also it seems that you have a 300W PSU. While that is what it was rated for new, time has passed and it most likely is not providing nearly that much power any longer, thus your next problem could very well be an under powered PSU. I would definitely not recommend upgrading his PSU (or trying to, I think this model Dell uses a proprietary unit requiring you to purchase from them or specialty shop).
Sorry for not having better news, I understand the (at times) frustrations with trying to breath life into an older system.