I'm still having hateful problems with my eMac. Looking on the Apple site for guidance, I found a thread which discussed the same problems I'm having: of sudden freezes after coming out of sleep mode. It could be the capacitors on the logic board, which can deform, bulging out and leaking a brown substance. I had a look at the back, taking off the panel, but could see nothing amiss. And yet the symptoms described are exactly the same. So I don't know. I'm a total novice when it comes to the mysterious inner workings of computers. The only way to fix the issue is to replace the entire logic board. How I would go about doing that and how much it would cost, I've no idea. The computer is quite old and the extended warranty has long run out.