What was found
ON TAKEOFF, THE NOSE LIGHT ON BOTH PANELS REMAINS RED. HYD SYS 3 WAS NORMAL, RAN THE RED TAB PROCEDURES AND LANDING GEAR SHOWED 4 GEAR LIGHT WITH GEAR HANDLE DOWN. TRIED TO RAISE THE GEAR AGAIN WITH NO SUCCESS, RED LIGHT STILL ON WITH HANDLE UP. LOWERED GEAR AND LANDED. REPLACED NOSE GEAR RETRACT CYLINDER AND PROXIMITY CONTROL BOX FOR PRECAUTIONALLY.