you actually have the relay mod hooked up to the monitor and it is working with 100 uF ? i think you mean 1000 Uf right? 100 uf would be less than 10th of a second .....
I haven't taken my monitor apart yet so I haven't been able to test it with the monitor. Normally you hold the power button for about 1 second.
I know the 10k resistor works fine ... but try to turn your monitor on and off and then on again through the relay quickly. It takes about 10 seconds for the 10k resistor to drain the cap. You will see that it takes about 10 seconds for the relay circuit to reset.