When there are 2 vga sockets it means that there is the onboard graphics (built into the motherboard and can't be removed) and the other vga socket is from a separate graphics card that is plugged into the motherboard and can be taken out - and replaced with a new updated graphic card that has been purchased.
Were there any messages on the monitor? Did it say 'no signal' or somesuch?
Which pc have you got and what are the connections on back for graphics? is there VGA (blue socket), DVI, HDMI ??
And on the back of the monitor what connection ports are there? has monitor only the vga?