THE STUDENT PLT HAD BEEN AUTHORIZED BY HIS CFI TO CONDUCT A SOLO X-COUNTRY TRAINING FLT UNDER DAYTIME VFR CONDITIONS. HE DEPARTED KEY WEST AT 0330 EDT ON THE RETURN PORTION OF THE FLT. NEITHER HIS CFI NOR HIS EMPLOYER COULD OFFER AN EXPLANATION FOR THE 15 HR DELAY IN DEPARTING. WITNESSES, WHO SAW THE PLT BEFORE TAKEOFF, BELIEVED HE WAS INTOXICATED. ABOUT 45 MIN AFTER TAKING OFF, THE ACFT CRASHED & BURNED IN THE EVERGLADES. ALTHO THE WX WAS CLEAR, THE ACDNT OCCURRED ON A DARK NIGHT IN A SPARSELY POPULATED AREA WITH FEW GROUND LIGHTS. AN EXAM OF THE WRECKAGE REVEALED THE ACFT CRASHED WHILE IN A STEEP, INVERTED ATTITUDE. NO PREIMPACT PART FAILURE OR MALFUNCTION WAS FOUND. TESTS OF THE PLT'S BLOOD & URINE SHOWED ALCOHOL LVLS OF 0.25% & 0.32%, RESPECTIVELY. EVIDENCE OF MARIJUANA WAS DETECTED IN HIS URINE, BUT NONE WAS FOUND IN HIS BLOOD. A MED EXAMINER RPRTD HE HAD ISSUED THE STUDENT A CLASS III MEDICAL CERTIFICATE ON 6/23/86, BUT HE HAD MOVED SINCE THEN & COULD NOT LOCATE THE MED RECORDS. THE FAA RECORD CENTER HAD NO RECORD OF THE MED EXAM.