I think that I wrongly identified my problem as one with the security parameters on the shared folder. As I thought more about the situation, I finally realized that the NAS server, which created the shared folder, could not responsibly allow a network client to take ownership of it. It does allow a network client to create subfolders of the shared folder. The client does control these subfolders. I suppose that what muddled my thinking was that last October, for some unknown reason, the security parameters of my system drive (Drive C:) were changed to almost the same settings as the NAS shared folders. In that case, I was able to take back the ownership of the drive and restore the proper security parameters.
I think that my problem was probably that the drive mappings for these shared folders were no longer valid after the power failure. In any case, after I disconnected all of the drive mappings and restored them, things appear to work normally now.