Suddenly won't sleep

My desktop:

Whenever I attempt to put it to sleep, the two monitors go dark, but the rest of the system keeps running (all lights, fans active). It can’t be woken up from this not-sleep state as the mouse and keyboard do nothing; the monitors don’t wake up again so I don’t know if these input devices are asleep or I just can see them.

How do I begin to query the logfiles in an effort to resolve this? This is the one glaring hole in my Linux use. I used to be able to use the event viewer in Windows, and the KSystemLog only seems to show me the current session.

The only solution so far has been to brute force restart, and that’s not good so I have been shutting down instead of putting to sleep. Any advice appreciated.

edit: this is not a new system. Has been running along smoothly for months, and I can’t relate it to any particular update.