How can you check to see if monitor cable, adapter and VGA connections are working? New computer, old monitor. Monitor was working with older computor. Have a DVI-A adaptor connecting new cable to VGA monitor.
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First boot the computer into "safe mode". (use F8 after you see the Windows logo) Safe mode will use a standard vga mode of 800x600 and 60 hertz. This should display on your old monitor. I suspect your default resolution settings on you new computer are out of the acceptable range of the old monitor.