Where does all the power consumed by a CPU go?
In the CPU it's all heat. It's the changing from 0 to 1 and back (which ultimately is what a computer does) which consumes the energy, because charge has to be moved from one place to another, and it's this current (moving charge) through resistance which causes heat. \$P = I^2 \times R\$

Ideally a computer which doesn't perform any tasks consumes no energy, but there are always tiny charge leaks and in a 1 billion transistor processor like a Pentium that combination of small leaks still causes a lot of power losses.