Q: Monitor will not come on after sleep.

Hi toothpiper, 

Thanks for stopping by the Apple Support Communities. I understand that you are having issues waking the iMac up from sleep mode. I depend on my iMac to be in proper working order. I'll be happy to go over some information with you that I found in this support article, If your Mac doesn‘t sleep or wake when expected.

If your Mac doesn't wake when you expect

Your Mac might pause a few seconds before it wakes up. If it doesn't seem to wake at all, check for these possibilities:
Your screen brightness might be turned down.
If you're using an external display, your display might be turned off. 
Your Mac might be in safe sleep. To wake from safe sleep, press the power button.
Check for a sleep indicator light, if applicable, and make sure that your Mac isn't turned off.

If the previous steps don't work

These additional steps may help identify or resolve the issue: 
Reset the SMC.
Reset NVRAM.
Disconnect external devices other than your Apple keyboard, mouse, and display. If that resolves the issue, gradually reconnect your devices, testing each time, until you find the device that is interfering with sleep. Then check the documentation that came with the device, or contact the device manufacturer.
Start up in Safe Mode to see if the issue is related to non-Apple startup items, login items, or kernel extensions. 
Try to isolate the issue by using another user account. 

Also, OS X El Capitan: Revert to a previous OS X version, goes over the steps required to revert to a previous OS. Please note that any changes that you made since updating the OS will be lost. 
 

Have a great weekend!