I have bought an used I7 7700K and my system does not Post.
With my old I3 6100 it works completely normal.
The BIOS ist up to date (latest version).
Mainboard: MSI Z170A SLI
500W Power supply (Coolermaster)
Is it really damaged?
If one processor works and another doesn't -- and you know that the processor is supported by both the motherboard (and its BIOS) and the systems cooling solution -- then there is a good possibility of that other processor being damaged.
With the information provided, we cannot say for sure; you have to determine this and you have to rationalize this determination with the seller...