Your desktop simply cannot start because even though current is flowing through the motherboard and other critical components, it will not start without the CPU, a.k.a the Brain of the operation.
All computers run through a POST in which it systemically checks if everything is in place, i.e it beeps when some problem occurs or something is damaged or unidentified, so it checks itself before it proceeds. There should be no damage from you powering it on without a CPU, although it is not recommended that you do.