Hi Dave,
I've not (yet) experienced the effect you get, if my Mac is not working properly it will usually but not always just stay on screensaver.
For your info my system is iMac desktop, Apple TV, Time Capsule and iPad mini on which I use Remote App to play music through Apple TV and then speakers, just recently an electrician came to the house to check on replacing kitchen lights while I was out, apparently he had power on and off 6 or 8 times in about 10 minutes, after that Apple TV was very poorly, rebooted it still didn't work. I decided to do a full reboot of everything in the order that one of the AppleCare guys told me was best, shutdown and unplug my iMac unplug router and Time Capsule unplug Apple TV shutdown iPad
Reboot in this order, plug in router (wait five minutes) plug in Time Capsule (wait for solid green light) plug in iMac (wait five seconds) power on iMac let it start up fully then plug in Apple TV and let that reboot, finally reconnect iPad.
Screensaver, display sleep and computer sleep all worked perfectly for about two weeks then went to pot again, if screensaver worked it would stay on screensaver and not shutdown, if screensaver didn't work then display sleep and computer sleep would work.
If I reboot and reset SMC it all works again for a while then goes weird on me again, I've given up trying to work it out, there seem to be too many variables.