Actually.... I've played COD2 on a laptop with a 965G graphics card. It worked quite well at low detail, so your G33/G31 graphics card should be able to run them as well.
However, if you want to play more games, I agree you should invest in a proper videocard and power supply. Just make sure you can actually fit them in. In the past, I've seen big-brand computers (Dell) without AGP slots, and wouldn't be surprised if your computer can't fit a modern PCI express videocard.
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