Backup failing in error code 13 (only for / file system)

sounds like a stale mount problem. reboot or try Joe's method

How to fix stale NFS mounts on linux without rebooting
http://joelinoff.com/blog/?p=356

See, NetBackup has no issues as it is backing up defined streams with no problems. But when root or " / " is used then the backup fails. All Netbackup is trying to do is traverse its directories and it cant do that due to a stale file or something wrong in the filesystems. This isn't a backup problem. It is a filesystem problem.

what about the du -sh /* command output.. does it compleating successfully ? how much time its taking...?

and also check ls -l / too..

if those commands did return normally the promt as df -k .. 

reboot would be the another option with FSCk check.. 

The 'du -sh /*' and 'ls -l /'commands are not displaying any information since 2.5 hours.

This is proof that the problem is at OS level, not NBU.
NBU needs similar information in order to backup / filesystem.

Have you logged a call with OS support team?