Connecting dual monitors on Mac Mini (mid 2011)

I am attempting to connect a second monitor to my mid-2011 Mac Mini. Multiple attempts and fixes aren't working. I could use the wisdom of the readers, here. My two monitors are:

Dell S2230MX, attempting to connect with a DVI-D to HDMI adapter into the Mini's HDMI port

AOC e2243Fwk monitor, attempting to connect with a VGB cable (with Thunderbolt adapter) through the Mini's Thunderbolt port.

The AOC monitor works fine. The computer performs as if it *wants* to recognize the Dell monitor, but just won't do it. Multiple attempts at mirroring displays, changing resolutions, etc. have been futile.