This will not work.
Perpetual motion implies infinity.
Solar cells, as well as other electrical components, do not last forever.
Specific to your idea, you lose efficiency of work through every step of the process. As you said, LEDs and any other electrical transmission system will give off heat which will be lost regardless of the LEDs being placed in a vacuum. Solar cells operate at an efficiency of
6% to 42.8%.
It's simply not possible.
