restarting computer deleted photo settings in camera raw

If the parametric edits were written, you're fine and you should see the edits when reopening them in ACR.

If they were not saved due to the shut down, then no, they never got saved. Not knowing what exactly 'shut down' process was used (you actually did a quit and shut down; everything should be saved. The computer froze and shutdown, not so much), can't say for sure. 

There should be no reason you can't find the original raws, at least ACR has no means of deleting them, but the ACR edits, that's a different story.