Well I'm Confused at the replies.
As far as I am aware a MAPt only applies to non precision approaches, and DA/RH apply to precision approaches. For an ILS app the DA is an altitude, not a point on space, so if you reach your DA and are not visual, you must carry out a missed approach. So in the case of a DME failure for an ILS, the distance is not needed, if you are within tolerances on GS and at your DA.
AIP ENR 1.5 1.10.1
$0.02