System Sleep Wake Problem - My Imac doesn't turn on

Hello.

All started when I accidentally unplugged the IMac while it was on. After that the computer didn't turn on no matter what I tried to do. I had lost hope when after about seven days the computer turned on by itself without me touching it! The message it showed me was that "System Sleep Wake experienced a problem". I used the IMac for a while and everything seemed to be going well.

When I turned off the IMac, I had the same problem again. It doesn't turn on again.

Any idea what the problem is or what I can do to solve it?