It's a proprietary power supply, you will have to get it from Alesis or an auth'd service center, or try to get one from ebay. Good question would be why in the H-E-Dubble-L did they make the darn thing that way in the first place?
I'm not sure how you "came into" this mixer, but I hope you dont have any problems with it. If you can do so without losing a ton of money, you would be better off selling it and getting something more reliable. Or you can get a second one for parts. It is very easy to work on if you have parts. This is the one piece of Alesis gear that I have always been very unhappy with, and their old service dept really took me for a ride with the thing. But they've been sold and bought now so the service is much better, but this mixer will still go to a third party service center.