I have an HP 1 gb ram, intel celeron 3.4 gb processor and 256 mb geoforce 6600 graphics card. Yet on certain games it crashes after 5 - 10 minutes

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I have increased the virtual memory and defragged twice yet it is still doing it. Oh I have checked requirements on the games before playing them (Maybe dim but not that dim :-)
Is there anyone who can give me some help on this as I am beginning to think the only way out of this is to buy a new one.
Thanks