SQL Server Rebuild/Reorganize Fragmented Indexes causes CRC error or consistency errors
The operating system returned error 23(Data error (cyclic redundancy check).) to SQL Server during a read


This indicates the operating system detected an issue reading data from the hard disk itself.  When data is written onto the filesystem, the operating system calculates a CRC code for each block written; when that data is subsequently read back the operating system performs the CRC operation again on the read data and compares it with the CRC stored in the filesystem.  If these two CRC codes don't match the OS reports error 23.  I'd be very surprised if there isn't a hardware issue with either the drive itself, or perhaps some other component such as the motherboard or drive controller.  

WITH (ONLINE=ON) in the Enterprise Edition of SQL Server will have no effect whatsoever on this issue.  Online index operations vs offline index operations are no different at the operating system layer; data is read and written as necessary to either rebuild or recreate the index.