While en route, the acft's ELT suddenly activated. The plt made an unplanned landing at Laguna, NM to correct the ELT problem, then he continued on to Coronado Arpt at Albuquerque, NM. He said this incident made him tense. After receiving radar vectors to the arpt, Apch control issued a last minute warning that Rwy 17/35 (the main rwy) was closed at Coronado. The plt was unable to receive a response on the Coronado UNICOM freq; however, based on an advisory to another acft, he elected to land on Rwy 21. During the apch, the acft was high & fast. It touched down about 1/3 of the way down the rwy. The plt raised the flaps & applied brakes, but was unable to decelerate as fast as he expected. To avoid hitting a fence near the end of the rwy, he applied left brake & rudder & the acft went off the left side, hit sand & nosed down when the nose gear collapsed.