Here's the error from the Backup:

BackupIoRequest::WaitForIoCompletion: read failure on backup device 'T:\Data\T2KAdmin.mdf'. Operating system error 23(Data error (cyclic redundancy check).).

We're going to be running a DBCC CHECKDB but it takes 8 hours to complete (305 GB DB).

We had another idea: since this page is now not used by any object since rebuilding the index, if we shrink the data file that disk block could be reallocated back to the operating system and not be in the data file at all any longer. Then our backups should work, right?