Because before the drive failed, I have seen a couple of times that the bak file is only a couple of Kbyte while it should be around 200 MB. At that time I ran the backup manually then I could get a good backup.
So, no I don't know 100% that the backup it corrupted but since the data hard drive had gone bad and for the fact that it had backup problem before I think most likely the bak file is corrupted too.
Sorry I don't know about the recovery model.
Thanks,
Howard.