A slignbox does not control a TV; nor should it. It controls and displays a component or source such as a DVD player, blu-ray player, cable box, satellite receiver, cable or off-air connection (in the case of a pro model), etc.
It would make no sense to output from your TV itself to a slingbox and have the slingbox control the TV which would have ti come on when no one is home and the slingbox is accessed remotely.
Addition: Problem solved - the codes for 32PFL5604 worked after all.
I thought, that that's what 'remote viewing' meant - to be able to control your TV from a distance ;-)
Joke aside - as I wrote in my post, my TV contains a built in DVB-T tuner - and it's obviously this, that I want to control and stream - and it's controlled by the remote, that also controls the TV itself.
(The TV has a SCART out connection, that e.g. can be attached to a DVD recorder - or in my case the Slingbox)