external mic was plugged

An external mic was plugged into A D5100 but the mic was not turned on, is there anyway to retrieve audio?

No. When you plugged in the external mic, the camera mic was disabled.
External mic was off, so no audio.

test, test, test... and when you think everything is working, test again....

I've only done a couple of video wedding shoots for friends, but my number one rule is enable audio level bars on the display if you have that option and use a lightweight set of headphones. You want to actually hear what is being recorded and if the mic input is being overloaded or not. I stopped using Auto audio level control too. It gives nasty pumping audio and background noise. Far better to manually drop the mic levels slightly and bring up levels in post if necessary.