maybe you are focussing on the wrong part of the board, the LC III will start without battery, the capacitors you replaced ( C2, C4, C5, C7, C8, C13, C18, C19, C20, C21, C22) , FPU, RAM simm and VRAM extension
could you test the board without battery, FPU, RAM simm, VRAM extension
could you...