Can you give some details on what kind of hardware and software you have?  PC or Mac, what operating system, what processor and wattage of power supply, what kind of video card etc?  Does it ever give you any kind of alarming dialog box?  Is there anything like a pattern of events that you can see that comes before the crash e.g. during rendering, moving files or the like?  To me, your crash problem sounds like it could be caused by a lot of things:
overheating video card (I've had this happen and it can make the screen go haywire like you describe)
failing power supply like already mentioned, or possibly its wattage is too low to drive all the hardware bits you have installed

Those are the two big items imo, but it really could be a lot of things.  If you are running Windows XP, you can try looking in the Even Log (Start Menu -> Settings -> Control Panel -> Administrative Tools -> Event Viewer, and look in the System log, or possibly Application) ... look for Errors (red circle with a white X in it).  Maybe you can find a little information there.

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