A Manhattan man died of an apparent overdose after an ambulance failed to show up at his building for more than an hour, forcing frustrated cops to finally rush him to the hospital, to no avail, police and law-enforcement sources said.  Adam Benhammou, 22, of East Harlem was showing signs of an overdose at his building on East 116th Street near Lexington Avenue at 5:13 p.m. Saturday when a 911 call was made asking for first responders’ help, according to authorities and sources.  Adam Benhammou, 22, suffered an apparennt drug overdose in this East Harlem building Saturday. Google Maps When NYPD officers arrived at the scene at 5:40 p.m., they found Benhammou “having trouble breathing and acting erratic,” sources said.  Four minutes later, the cops radioed for an ambulance to come in “a rush,” according to the sources.…