The present PSU from new only had a three year warranty so may be showing it`s age
** the fact that it can power the 9600k doesn`t come into the equation until the GTX 1080 is in the board, this because even the none Ti version of the GPU
** requires almost twice the wattage that the CPU does and that is when the processor is under a full load.
** The none Ti version of the GTX 1080 only requires 1x 8-pin supplemental power dongle from the PSU, specs
here you mention that your GPU requires 1x 6-pin + 1x 8-pin, this suggests to me that you have the Ti version which requires a minimum of a 600W Gold efficiency rated PSU, the Ti version also requires more than double the wattage that the new Intel CPU requires, 250W to be precise, you can confirm this for yourself
here.