GFI trips when turning on a computer with the monitor on but not when the monitor is off
If the GFCIs have a 5mA threshold, the reason  might be related to the cable capacitances. Domestic cables can accumulate 200-400 nanoFarad per kilometer, i.e. the GFCI could trip if the summed up downstream cable length is 500m , if the voltage is 120V, 60Hz. Without any devices plugged into the circuit. 

The usual PI-filters of switch mode power supplies in PCs and monitors can add more capacitance, increasing the tripping probability. This is why those 5mA GFCIs seem to be too sensitive in some cases, thus providing not more safety then a 30mA GFCI, but instead are the reason for a safety gap if the annoyed user eliminates that 5mA GFCI if it tripped again just before he was to top his high score in the difficult PC game after weeks of failed sessions.