On my windows 8.1 computer, when I connect a second monitor the first monitor goes blank (loses signal) and won't come back even if I unplug the second monitor. I can plug either monitor into the primary video port and it will work, but the second video port doesn't appear to work at all. Graphics card is an AMD Radeon HD 7900 series Monitors are both Asus VGA monitors.
I've seen cases where plugging in a new monitor shifts the primary monitor. That could be what is going on.
This is reset by going to the Control Panel > Appearance and Personalization > Personalization > Display Settings > Monitor tab
"I can plug either monitor into the primary video port and it will work"
Did you try ⊞ Win + P to either extend or duplicate the monitor output?