Well, you've come at the right time since I dug deep into this system last weekend.
So, the good news first--your data should all still be intact, and Intel released a technical paper and how to retrieve the data using unix. It's not for the faint of heart as it's quite technical, but it can be done.
So now onto the potentially bad news. Power supply failures can be catastrophic and damage the motherboard or other components, which might have happened.

But it could also just be the dom not booting, which is easier to fix.
I'd remove your drives and try the reset a couple of times to see if you can get the dom to boot again. The types of presses also do different things per the ss4200 wiki here:
http://ss4200.pbworks.com/w/page/5122739/Boot Issues - Power light flashes continuously
If you're able to get the DOM to boot again, you're halfway home.
If not, you can remove the dom and put it in another system and then re-image the dom as it might be corrupted. I think technically you could even put the image on an ide hard drive or compact flash with a flash adapter, but I'd try the original dom first.
Once you have the system booting again (even if it is in pieces), you can put your drives back in it and there's a process to make it use those drives without formatting them. There's some instructions I've saved from somewhere that told me how to properly do this, but I can't recall atm. BE CAREFUL HERE BECAUSE IT WILL WANT TO YOU REFORMAT THEM, AND YOU DON'T WANT TO DO THAT OR YOU WILL LOSE THE DATA.
Let me know what happens and I'll do my best to help.