Dead RN104, is data recovery possible?

The power supply does sound like a probable cause of your issue since it won't power on at all.  It is unlikely a power surge would make it though the external power supply and harm the NAS, at least without also doing damage to the supply.  That the LED on the supply lights without any flicker isn't that good an indication it's OK.

Now, I'm only talking about a surge that came in on the power line.  If you had a very local lightning strike, it could have come in via the local ground, and that's different.

If it turns out not to be the supply, then you'll have one if you go to buy a used ReadyNAS, some of which don't come with the supply.

Note to everyone:  At my home, the cable company (aka network provider) sunk a separate ground several feet from the power ground.  That's a bad thing for a local lightning strike, as those two grounds could momentarily be at different potentials and current would flow through the path of least resistance, which could be your TV, cable modem, or whatever.  I ran a 0 gauge wire between the two to be the new path of least resistance.  Don't count on any surge protector for a local lightning strike.  That bolt just traveled 5 miles or more through air -- a little surge protector isn't going to stop it now.  But some surge protectors do have a warranty that replaces attached devices, so maybe there is some value in this case.  Of course, I do live near the lightning capital of the US.