I have a similar problem, except instead of shutting things down, static discharge seems to wake my computer up (from suspend-to-ram). I have yet to figure out why that happens, but it's not the mouse or keyboard.
My guess is that, in the vein of the "monitor flickering" symptom, your PC sees the DP/HDMI cable disconnect and reconnect due to the static. The reconnection wakes it up.
I don't know. Manually {dis,re}connecting the cable doesn't wake the PC up, but it's too hard to reproduce reliably to tell if having it disconnected makes a difference.