The aircraft, with callsign CFG3228 was inbound from Hamburg and entered the Canaries FIR at 10:21 some five hours into flight. ATC assigned the aircraft the standard terminal arrival route (STAR) TERTO6H, used for landing on runway 26 at Tenerife South. Shortly afterwards, as a result of weather conditions at the airport with lightning and shifting winds, the tower changed the runway in use from 26 to 08. Upon doing so, problems were detected with the ILS equipment. Another aircraft on final also reported to the controller problems with receiving the glide path (GP) on the new runway. Maintenance technicians who were dispatched to the location of the equipment confirmed That the GP and the DME on the ILS were not transmitting. The aircraft was diverted from the initially assigned STAR to go around the south side of a storm system and continued on its approach so as to capture the localizer for the new runway. ATC then informed it that the glide path on the runway 08 ILS was inoperative, so the crew altered its initial plan to make an ILS approach and prepared to do a non-precision (LOC DME) approach to runway 08. The crew, which was not informed that the DME on the runway’s ILS was also inoperative, erroneously used as its reference distance to the touchdown point the VOR DME callsign TFS, located along the coastline, 5.7 NM before the runway. With that reference distance, the crew started the final descent early with neither the crew nor ATC detecting the vertical deviation in the flightpath. While on final approach, at a radio altitude of about 435 ft and 6 NM away from the runway, the EGPWS terrain conflict issued a warning. The crew reacted by aborting the approach and, in light of the bad weather, opted to divert to Fuerteventura, where they landed without incident.