AFTER MAKING AN ILS APPROACH TO RWY 16, THE PLT WAS CLEARED TO CIRCLE AND LAND ON RWY 34. AS HE TURNED FINAL, HE WAS TO THE WEST SIDE OF THE RUNWAY AND WAS TOO HIGH TO LAND, SO HE MADE A LEFT TURN-AROUND BACK TO RWY 34. TOWER PERSONNEL TURNED THE RWY LIGHTS UP TO HELP THE PLT LOCATE THE RWY AND CLEARED HIM TO LAND. THE PILOT STATED THAT HE HAD COMPLETED HIS PRELANDING CHECK, AND TO THE BEST OF HIS RECOLLECTION, HE HAD EXTENDED THE GEAR AND EXTENDED 20 DEG OF FLAPS. HE DID NOT RECALL RETRACTING THE GEAR WHEN HE MADE THE 360 DEG TURN. SUBSEQUENTLY, THE PLANE WAS LANDED ON RUNWAY 34 WITH THE GEAR EITHER FULLY RETRACTED OR PARTIALLY DOWN. THE PLT STATED THAT A WHEELS UP LANDING WAS MADE WITH THE GEAR HANDLE DOWN. SCRAPE MARKS WERE FOUND ON THE UNDERSIDE OF THE FUSELAGE, BUT NO SCRAPE MARKS WERE FOUND ON THE GEAR DOORS. WHEN THE PLANE WAS JACKED UP AND HYDRAULIC PRESSURE WAS APPLIED, ALL 3 GEAR BEGAN TO EXTEND. HOWEVER, THE GEAR MECHANISM WAS DAMAGED AND WOULD NOT OPERATE PROPERLY.