WHITE HOUSE CRASH . . . RADAR, BUT NO HEADS UP

The facts are trickling in about Frank Corder's fatal plane crash, and they seem to add up to one conclusion: a president can never be entirely protected, even at home. For those responsible for providing that protection, some of the details coming to light are particularly embarrassing. For instance, minutes before Corder, 38, smashed onto the lawn and skidded into the White House early Monday, radar at nearby National Airport reportedly detected the plane. Yet, officials did not notify Secret Service agents who guard the mansion. Federal investigators are probing airport records to learn why.A MATHIAS RUST WANNABE? So why'd Frank Corder do it? He appeared to be depressed by the death of his father and the recent breakup of his marriage. What's clear is that he had a history of alcohol and drug abuse, and died with a .045 blood-alcohol content, just a smidgen above the legal limit for pilots. His blood also showed trace amounts of cocaine. Relatives said Corder might have had publicity in mind because he once talked admiringly of Mathias Rust's 1987 landing in Red Square. A brother reportedly was told of a suicide plan.