own nav

Let me first say, as far as the interview question goes, it seems to imply you are out of radar contact and have no GPS, so if that's the case, I'm with the climb to MSA while turning ten, twisting ten crowd, proceed inbound and go missed.

I'm pretty sure my company would like to see at least a little trouble shooting, ie switching to your other receiver. Use your audio ID to check it, bear in mind that the DME doesn't ID every cycle so it may take a few seconds. You could also try tuning to another DME (might even try an ILS DME in the area) just to see if it's your reciever or the ground equipment. It might not solve your problem, but I'm sure your maintenance department would appreciate your input in fixing the problem, especially it caused a service failure because you had to divert.

If it is the fault of the ground equipment, 91.183 (c) requires that you report anything "relating to the safety of flight" to ATC while IFR. I'm sure they'll want to verify it with other aircraft before they issue a notam, but it's your responsibility to give them a heads up. If you can make it in using your GPS, great, but you still need to make the report.