Actually BDAqua has looked at the wrong model of Mac mini, the model of Mac mini you have does not have a Thunderbolt interface it has a Mini Displayport and a Mini DVI. You are currently using a Mini Displayport to HDMI adaptor.
You should be able to use a Mini DVI to VGA adaptor such as this http://store.apple.com/us/product/M9320G/A
Alternatively, you could use a Mini DVI to HDMI adaptor such as this http://ukhdmi.com/Mini-DVI-to-HDMI-Adapter_QQ101738 along with a Mini Displayport to VGA adaptor such as this http://store.apple.com/us/product/MB572Z/A
I believe your Mac mini is a Late 2009 model and the correct video specs would be as follows
- NVIDIA GeForce 9400M graphics processor with 256MB of DDR3 SDRAM shared with main memory3
- Extended desktop and video mirroring: Simultaneously supports up to 1920 by 1200 pixels on a DVI or VGA display; up to 2560 by 1600 pixels on a dual-link DVI display using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)
- Mini-DVI port
- DVI output using Mini-DVI to DVI Adapter (included)
- VGA output using Mini-DVI to VGA Adapter (sold separately)
- Mini DisplayPort output
The webpage for the full specs are here http://support.apple.com/kb/SP577