Today the icon is on the System Tray without the red "X", but the remote isn't working at all.

I'm selecting pre-existing make/model profiles. What do you think about removing all my previous configurations/apps/etc and starting all over again?

Thanks for your help.

That might be a good idea at this point. I would also suggest bypassing the pre-existing make/models, and choosing custom, and then "learning" the buttons of the remote, assuming KRemoteControl supports this functionality.

Ok. I'll reinstall it and keep you informed of the results. Could you please tell me all files - and their directories - that you remember I need to remove manually in order to have a fresh reinstall from scratch?

Thanks for your help.

I would suggest simply removing all "remotes" through the KRemoteControl user interface, which should achieve the desired result.
It is not necessary to delete the configuration of other applications.