|NOTE that you usually must use either the VGA connection or the DVI connection to a monitor if it has both types of ports - connecting both will not work.|
If the DVI port on the older computer is the secondary port, not the primary port, you may need to enable it's output.
Connect a monitor to the VGA port.
Connect another monitor to the DVI port.
Boot the computer, and when the desktop screen has loaded, RIGHT click on a blank part of the desktop screen, select Properties.
Click on the Settings tab.
Hold your cursor over the two displays, one at a time.
Whichever one displays "Not Active", RIGHT click on it and Enable it or whatever.
You should have video on the DVI display.
Windows will retain that setting as long as that monitor is still connected to the computer's DVI port while Windows is running.
If that doesn't help you need to supply a lot more info.