The law of Conservation of Energy says all that input electrical energy going into the system has to be accounted for in the form of some other energy.

Now the only thing moving will be the fans and the hard disks, which means only a very little of that input energy will be converted to kinetic energy.

The system will not be storing energy, meaning none of the input energy is being converted to potential energy.

Now some energy will be lost in the form of noise and light emitted from the leds and monitors etc.

So that only leaves the radiated energy (i.e. the heat) produced by the system.

I would think that heat component would make up the largest portion of that energy pie.

Even the kinetic energy (fan motors, HDD motors) eventually becomes heat. E.g., the moving air from fans dissipates its energy in turbulence in the room's air, and in a closed system (airtight room), the resistance to airflow (resulting in heat) must equal the pressure differential created by the fans, unless the air builds up unbounded speed. Likewise, torque to keep the HDD platters spinning will be exactly equal to frictional losses once the disks are spun up, so all power into the spindle motors becomes heat.

Even noise that leaves the system either becomes heat as the pressure waves dissipate through the atmosphere, or else do work on eardrums (mechanical energy) which eventually becomes heat as the inner ear resists the motion of the ear bones :-)