...then dinosaurs would "weigh" around 4.5% less than they should at today's gravity. Totally explains why they all died...as the earth started slowing, they eventually became too heavy to survive and all sank into the earth to become fossils. Quick! Get me some paper! I'm publishing a new textbook!

How much do you think that the capacitors have drained? I'd bet that the capacitor drains as much energy during the switched-off state as the monitor would draw without any relay. That energy has to be "recharged" from the grid (or solar panel) when the monitor comes back on.

I agree with the original post: Electricity can't be produced from nothing. (Solar cells are magic aren't they?)

A solution would be present even without the relay:
If the solar panel on the monitor supplies enough energy for the microprocessor to function, then even if the relay from the monitor was removed, the monitor would still draw 0 power (or even make more than enough to run the power back OUT of the monitor) and you wouldn't have the added complexity of the relay and other electronics in the system.

Concentrate on making devices more energy efficient, don't concentrate on drawing 0 power.

CONSERVATION OF PROBLEM - Don't fix something and break two others.