That nothing is being written to tape.  If you are seeing the KB/s field increment, I would assume your backup job is writing to something. 

Have you checked to make sure it isnt writing to an incorrect storage unit?

have you verified that the disk space on the client is not full?

There is more than 300GB free space

and there is no kb written

The storage Unit is ok.. there is another backups running  

Dont cancel the policy and see what the error it gives to you then share that error 

Create a test policy (without BMR) to backup a small folder on the client. Ensure that bpcd and bpbkar log dirs exist on the client.
See if this policy runs successful. bpcd log will confirm that comms have been established and bpbkar will log data sent from client to media server.
Once this policy runs successful BMR process flow can be checked.

About access control on Windows - the backup runs under the account specified for NeBackup Client service. The default is LocalSystem and is suficient under most circumstances.

your EMM would have gone to stale state.. this was seen in many sites.. try deleting all the drives, robots,storage units and reconfigure them. this will clear all the stale entries..

this would generally solve your problem. or else there is command to reset the emm

what exactly happens here.. when a job starts NBPEM(netbackup policy manager) gets all the info from BPDBM and asks NBJM(netbackup job manager)to start the job. NBJM will make a request to NBRB(netbackup resource broker) on the EMM, which wil use intelligent resource manager, then EMM will check for the available media and drives, storage units and allocates these resources to this job.
the these resources are marked as reserved, once these resources are allocated then it will inform nbjm and the job goes active and this process goes on 

  Now in this scenerio
when the job is complete is it is same nbjm which has to inform emm via nbrb that the job is complete and resources should be unreserved, but in certain situation where the instructions will go stale and emm will be in impression that the resources are still in reserved state and will not allocate to any jobs, due to which you will see this kind of problem on some jobs only

so inorder to correct to either reset the emm or reconfigure all teh drives which will release all the stale mappings.

I do understand the process flow. For this reason I believe the problem on the client side not sending any data. That is why I'd like to see the bpcd log to ensure that comms are established and bpbkar is started. In bpbkar we'll see if data is sent to media server.
If you look at the original post, it says 'it keeps writing'. This says to me that the resource allocation has taken place, bpbrm on media server has initiated bptm process which has mounted and positioned the tape and said in Job details 'Begin writing'. At this point in time bptm is waiting for bpbkar on client to send data.

BTW, stale resource allocations can be cleared with nbrbutil commands.