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 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 :-)
Not to mention heat pumps require somewhere to pump to/from, you can't just put one in your basement, plug it into the wall, and heat up the basement. Also heat pumps work best with mild differences, like say 40F inside and 60F inside if you want to heat.
Heat pumps reduce to space heater efficiency if it's sub-zero Fahrenheit outside I believe.
Although in the UK most people use gas to heat their homes, because its cheaper. I worked out once that gas and heat pumps cost the same in the end for the amount of energy. Although what I love about heat pumps is how quick they get a place warm compared to radiators.
Granted heat pumps need installation, or you can probably run a tube out the window with one of those adapters.
It's a silly hypothetical discussion, because for the price of this mainframe you could get a heat pump and a set of solar panels and a battery storage, and have some money left over for some Hawaiian shirts to wear once you've heated the place up.
For financial efficiency (environment be damned) a set of crypto miners would be better than either the mainframe or the heat pump.