The primary navaid used for the approach always appears in the approach title, but some States may not necessarily require title reference to any other navaids that may be required. Thus it's a matter of reading the plate in advance, as ooizcalling obviously did.
In this case, with a DME fix marking the MAPt., if the DME fails and you aren't visual, you need to execute a missed approach. You don't say which design criteria was used so, if it was TERPS, I may not be giving you the right answer. However, under Pans Ops, you need to maintain the altitude at which the DME failed (ie not below MDA) and track to the MAPt by DR, before following the missed approach.
This isn't especially critical if the missed approach goes straight ahead, but is very important if it involves a turn. How you find the MAPt by DR is up to you and, in an such an emergency I'd be inclined to use the GPS, if it had been running pretty close to the DME for distance info before the DME failed.
There's more options if ATC radar is available at the airport so I'd be telling ATC about the missed approach and requesting suitably safe vectors.
fatboy slim... a DME fix at the end of an outbound leg isn't always necessary and, in this event, the approach won't require it. If it IS necessary, a reference to DME is usually included in the procedure title.
I prefer things to be spelled out so that there's no chance of any misunderstandings. Thus, if I need to use DME in ANY part of an approach or missed approach, I'll stick "DME" into the title. Procedure designers in other parts of the world might have a different attitude though.