I was actively typing in a page when my computer crashed (I’m not sure why; one minute it was fine, the next it was down and restarting.) When I tried to get back to Scrivener, I got the following error message:
I’m kind of panicking now. Not only have I lost access to that project, but I’ve also got other projects and I’m terrified of losing those, too! 
Edited to add: I am running the most recent beta.
It sounds like one or more files Scrivener needs in order to open the project got corrupted in the system crash. Your closed projects should be fine, but we’ll need to dig into this one to see what’s the matter. First thing to check is the version.txt file, which is a little fragile and usually the one to go if something breaks. Happily, it’s easily fixed.
First thing, make a backup copy of your project (and call it something obvious so you don’t get them confused). Then:
Try then to open your project. Hopefully that will be all it needs and everything will be restored, voila, life goes on happily. If not, the easiest next step is if you can zip the project (the whole .scriv folder) and send it to support AT literatureandlatte DOT com so I can see what else got hit in the crash and recover what’s there.
I tried what you suggested, and it still didn’t work. I’ve sent the zipped file to you.
Thank you in advance for any help you can give me.
Just sent a reply with the restored project, looks hopeful! 
I had exactly the same problem. My machine sometimes shuts down and reboots for no apparent reason, even while I’m typing. I have sought help with Dell customer support but they couldn’t help me.
Anyway, MimeticMouton’s how to about restoring the project worked perfectly for me. Thanks!