However, you can get a vga switch. So that you can connect 2 vga(outputs) to one vga monitor (input).
When i google for vga switch, i see:
This ugly 2 way thing for 7 British pond(just to say it's cheap, because it's just a mechanical switch):
And this 4 way switch for 14 pond:
So go to computer (or electronic parts) store, and ask for a vga switch 2 way.
Or connect two computers with ethernet cable. Give computer with broken screen vnc server(so connect a monitor to install & configure that device(vnc) properly), and computer with good screen vnc client.
Oh this is very off topic compared to VLC for windows
