Recently, I have started to face this problem: I power on my monitor and PC, and there's no LED light on my Asus LED monitor (ASUS VH197). I have to wait for 5-10 minutes for the screen to show up after it's powered. This used to happen rarely - like once in a month, but now it seems to happen more often - once in a week or 2.
There also is another issue, where I turn on my PC, it starts, but within 5-10 seconds it turns off. I have to power it on again - then it works fine. I have a feeling that this could have to do with my power button on the cabinet.
My setup is about 7 years old, except for the PSU being just 2.5 years old.
PS: I don't keep my PC/monitor on standby - I switch on/off the power supply every time. Also, once the PC has booted up, there aren't any problems with either of the 2 hardwares.