Backup Database (SQL 2000 Compatibility) on SQL Server 2005 with CHECKSUM, but Page Verification TORN_PAGES Detection
Check the file permissions on the backup on the second server.  It's possible that's your problem, and it's easily fixed.  

If that doesn't fix it, you should run a dbcc checkdb on the original database, which will tell you if the database itself is corrupt.  

If DBCC returns okay, run a RESTORE VERIFYONLY FROM DISK = 'path to backup' on the backup on the original server.  

If all of that returns okay, go back to the second server and double-check the file permissions.