Here's the solution in our condo: We both keep our computers on all the time
But even with that our electric bill is not that much more. We have a stoneage refrigerator that pigs out more than a depressed Ricki Lake. Plus we tend to stay up late with the TV and lights on. Electric bill comes to $50-65 /mo. Does a computer use power? Yes. Is it as bad as you guys say? No.
My question is WHY does he leave the computer on? You haven't mentioned why. I leave my computer on because I am on the Internet serving files or downloading. If I'm not doing anything, I turn it off. If he's downloading or waiting in queue, I could see why he's loath to turn it off. But if his computer is not doing anything I see no reason why it has to stay on.
At any rate, the computer is the least of your worries. Make sure the monitor is off and the electric bill will be negligible. I'd be more worried about his lack of help. You both need to tell him that he's not pulling his weight. If he hears it from both roommates, maybe he'll catch on. If he's stubborn, you're right, violence is not the answer. BUT, if the lease is in his name, stick him with it and leave. Make sure to tell any potential roommates what a pig he is

If it's your lease, evict him.
But most of all, don't keep it to yourself because you'll just get more and more pissed off. I hate people who bottle up feelings and then suddenly explode out of the blue as if you were supposed to somehow know.