How can I connect two VGA monitors to a Mini using Thunderbolt and HDM adapters? I am running one VGA display using Thunderbolt/VGA adapter from Apple and it works fine.

Trying to connect second VGA display using HDMI/DVI adapter which comes with the mac using an additional connector DVI to VGA, but nothing happens!

I only have VGA monitors, so question is can this be got to work in some way ?
You cannot run VGA from the HDMI port the way you have it set up.  You need a direct HDMI->VGA converter.  The reason is that HDMI does not output analog signals.  The cable head actually has a digital-to-analog converter chip in it, but your HDMI&lt;->DVI adapter does not.  So even though the DVI&lt;->VGA adapter fits, the analog pins aren't actually connected.

Technically, the HDMI&lt;->DVI converter you're using was manufactured incorrectly.  They should have used a DVI-D connector, but they used a DVI-I instead.  A VGA adapter will not fit onto a DVI-D connector, but a DVI-I connector will accommodate anything.