Does it show up at all during boot up? That is can you see the boot messages, Dell screen, pre-boot or anything that just uses basic VGA mode? If no, your suspicion might be correct.

Since its old you probably only have an option to use a PCI video card or maybe an AGP video card. PCI video cards are cheap and you can put one in and use it instead of the onboard video. AGP a little more expensive and better, same option.

I'd try getting a used video card from a friend to check it out.

If it shows a screen on bootup you fixed the problem and all you have to do is disable the onboard video in the BIOS setup, uninstall the driver in the control panel and install the driver for the new video card and then go reset all your settings (right click on the screen and then properties).

Otherwise its a more serious problem.