Strange graphic-freezing problem even at start up

Hi all,
I'm not sure where to post this as I am not sure if this is a software problem or a problem with my monitor. I am posting this from my other computer, not the one I am having problems with as it has reached the point where it is unworkable for long enough to do anything with it.
Here is what is going on.
My computer is a Dell XPS 420 with a 17 inch color monitor. It was purchased in 2008.
On October 17th I started having issues while playing my DVD games. My computer would freeze up while the graphics onscreen would appear as rainbow. Sometimes the sound would continue on, sometimes it would freeze too. (DVD movies had no problems at all.) The monitor would act like it went into power saver mode. The only way to get out of the freeze was to turn off the computer. The Task Manager was impossible to get to.
I did a hardware check and a check with DirectX, but no problems were detected. I turned off the power saver settings. The problem continued anyway so I stopped playing my games.
On November 1st, I started having the same problems while online even while just in my email. The computer would freeze with the "rainbow" graphics onscreen. The only way to get out was to switch the computer off. The Task Manager would not be accessible.
On November 7th, the problem started when the computer was starting up. When I start up the computer in Safe Mode, the graphics appear in black and white horizontal lines all over the screen and strange color patterns appear.
The computer is off now and I haven't turned it on since then.

Is this problem with my computer hardware/software or is the problem my monitor? Also, if there is a way to do a diagnose for you my problem on the computer somehow, please advise me. I am willing to work with you, but I am unsure how to do that because my computer is not stable and could freeze at any time.
Thank you for your help.

 

Possible bad driver, or bad video chipset. You could try installing a pci-e video card and see if the same thing happens with the new card. Also, bad RAM can cause the problem, due to if the machine has onboard gpu, it shares the RAM.