Corruption won't be in the log backups anyway. Log backups contain changes made to the DB and, since the corruption was IO subsystem problems, it would not have been added to the SQL transaction log, which is what a log backup backs up.
I would recommend a restore from backup. This is repairable, but you'd lose data from two of your Orders tables and from the Logging table.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability