You want a utility which will launch a program (in this case miner) when computer is idle for x amount of time.
Here is one example:
http://appsapps.info/idlestart.phpNote I haven't used it, tested it, or even downloaded it. It is just an example. Likely there are other similar utilities which do the same thing. That is what you want to look for. Triggering off screensaver or monitor power off is dead end. Just look for utility which will start an app after x minutes of idle time.