Can I attach an Mac mini to a VGA monitor using an HDMI/VGA adapter? Can I attach the Mac mini to a VGA monitor using an HDMI/VGA adapter?

I have a new Mac mini I'm trying to attach to an old monitor that has VGA and DVI inputs. I have VGA cable and HDMI/VGA adapter and everything seems to connect fine, but the monitor doesn't see any input. The Mac mini works attached to TV using HDMI, but the TV also doesn't see VGA input if I try VGA (and HDMI/VGA adapter).

If this won't work, what will?

ADDITIONS: On further investigation it seems that I may need to use thunderbolt port to connect to VGA. I am having trouble finding thunderbolt to VGA adapter and would like to confirm that mini DisplayPort to VGA adapter is compatible.

Also, thanks to user3439894 for edits/improvements.
Does the adapter work with other devices? If not, then your adapter is likely broken. You should be able to attach an HDMI to VGA adapter to your Mac. Video adapters aren't computer/software specific. Side note, it would be a better idea to convert HDMI to DVI instead of VGA since HDMI and DVI are both digital, meaning they will output higher quality video, whereas VGA is analog, and will output lower quality video.