A single core Pentium and modern games at even low settings are simply things that do not go together. I suggest saving your money and getting a brand new system because this one will barely play those titles.
The games you mentioned wont even go off the ground with the CPU and RAM you have. Let alone fly with the GPU's you selected. Look up the minimum requirements of the games and see if they would work or not.
The g31 chipset supports both the 775 p4 and 775 core2 cpus. It looks like if you look for a bios update, there could be a new bios that updates the board to work with 775 core2 cpus.
If it does and you upgrade the bios to the new one that gives you support for the core2 cpus, that means you can buy a new dual core cpu for it like the woldale celeron 3300, or pentium cpus. A used 775 cpu like a core2-6800 or Q6600 would be good too.
-If you upgrade the cpu and card, then you will probably (you could try it and see if it runs ok with your current p/s first?) need a new power supply too. Something like a corsair 600 watt or antec 600 watt would be good.
Check and make sure you have a open pcie-16 slot and its not agp (some were agp). The best cheap card is the 800 shader hd-5770 or hd-6770 or nvidia's geforce 460. (just buy the cheapest on on sale out of the three).
If you can't upgrade the cpu, i would get the cheapest card out the three you mentioned. The hd-4670 does ok and is usually cheap.
You will have to stick to a bit older games like serious samII, the first few call of duty games in the series, fear, prostreet on med settings, UT3 engine games should still run like UT3, batman, ect but the load times will be horrible, i would try the playable demos first to see what runs.
The gt240, 9800gt, hd-4670 are all too slow to play any of the games you mentioned. But the 9800gt is the fastest of the 3.
If you can upgrade to the core2 duo, the hd-5770 are your best cheap cards.
The geforce 460 paired with a core2 will give you the best combo here.
Without the cpu upgrade, you are cpu limited to about the gt240, hd-4670. The 9800gt will still work but it will be held back by the p4 cpu.
The core2 is about 4 times faster than your current p4 cpu.
I would check and see if there is a bios update to let your board run core2's first. Before spending money on it, follow the instructions, flash your bios to the new one.
Flashing the bios carries some risk, if it goes wrong you can end up with a dead board. Your board is outdated anyway so its worth the risk. I would do the bios flash first, if it is is successful, then buy the new cpu.