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Ah that's the problem, the graphics card is built into the motherboard and uses system memory for it's own use, thus lowering the amount of RAM avaliable to your total RAM minus the graphics card's memory, so 192mb. The reason the games won't play is probably due to the fact that the card's not really very good.
You can try something, if you can get into the BIOS settings (usually by pressing delete as soon as you start up the computer) if you hunt around there *should* be an option to change the amount of memory the graphics card is using (this will only apply if it is onboard, but I'm about 90% sure it will be), if you lower this to 16 or 32mb, you should see an increase under your system properties in the control panel.
Also, is the slot where your graphics card fits in a different colour to the other slots?
And have you got an onboard graphics card?