THE PLT REPORTED THAT HE 'TOPPED OFF' HIS FUEL TANK WITH 12 GAL OF FUEL AT HOMESTEAD, FL. HE THEN FLEW TO THE PORT LARGO ARPT AT KEY LARGO, FL AND TO THE MARATHON ARPT, MARATHON, FL, BUT DID NOT REPORT OBTAINING ADDITIONAL FUEL. WHILE EN ROUTE BACK TO HOMESTEAD, THE ENG LOST POWER. DURING A LANDING IN A CYPRESS SWAMP, THE LANDING GEAR SUNK IN DEEP MUD & THE ACFT NOSED OVER, AN EXAM OF THE ENG REVEALED NO PREIMPACT/MECHANICAL MALFUNCTION OR FAILURE, EXCEPT THAT THE CABLE FROM THE BATTERY TO THE STARTER WAS BROKEN THRU 70% OF THE WIRES. THE PLT NOTED THAT THE STARTER WOULD NOT TURN THE PROPELLER WHEN HE ATTEMPTED TO RESTART THE ENG. ALSO, THE ELT BATTERY WAS OVERDUE FOR A CHANGE & THE ELT DID NOT WORK. HOWEVER, THE DOWNED ACFT WAS SPOTTED BY ANOTHER PLT & AN AIR FORCE HELICOPTER WAS DISPATCHED TO EVACUATE THE PLT & PASSENGER. THE ENG WOULD CONSUME APRX 3.7 GAL/HR AT 75% POWER.