I think that would be wise troubleshooting. If the BeoVision 4 was faulty or if the control cable between the BeoVision 4 and BeoSystem 3 is faulty, the commands from the Beo4 remote will not be reaching the BeoSystem 3.
If would be a good idea to check the BeoSystem 3 by using an external IR receiver. As I mentioned before, the wires inside the IR sensor are very fragile and break or pull out of their connection quite easily. You should examine them to make sure the connections are good. Also, the inputs on the BeoSystem 3 can be a little confusing. If you haven't already, you should download the user guide
Once you have an external IR receiver connected to the BeoSystem 3, you can access the settings by pressing MENU, MENU on the Beo4.Once you have entered that, pressing 0,0, GO will take you to more advanced settings. Use caution in making changes in the advanced system settings, though.