The screen goes black and the mouse turns off after 30 seconds...?

I have an old Dell computer. The screen started going blank because there was no signal and my usb mouse turned off both after about 30 seconds. Then I turned it off completely, and the computer won't even turn back on. Then I unplugged it and plugged it back in. The computer then gets to the point I got it... show more I have an old Dell computer.
The screen started going blank because there was no signal and my usb mouse turned off both after about 30 seconds.
Then I turned it off completely, and the computer won't even turn back on. Then I unplugged it and plugged it back in. The computer then gets to the point I got it to the first time, and then I have to unplug it and plug it back in to get to the same point.
I tested the hard drive by unplugging it and used a linux live CD. The same problem occurred, so I'm sure it's not the hard drive.
A computer technician told me that the problem is the video card.
If it is, I need a way to fix the card because it's part of the motherboard. It's not something that can be removed.
I know that a video card has ports for the monitor and other components attached to it, and those ports are attached directly to the motherboard.

Thanks For Your Help
Update: I don't use Windows on that computer. I use Fedora 10 (a Linux distro)
I can't access anything on the computer that involves turning it on.
The video card, as I said before, is part of the motherboard.
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