LCD goes off for a moment
We can only guess, but maybe the fan draws significant startup current.  If the wiring in the house is poorly set up, then that can cause a momentary dip in line voltage at nearby outlets.

It may be that the monitor is not capable of riding out the short dip in line voltage.  Your "CPU" (whatever that really means), may have more bulk energy storage in various places of its power supply.  This supply is capable of maintaining the DC voltages that keep the system running despite the short dip in input AC line voltage.