The only thing that might not work reliably is being able to control the sound system from the TV remote which you may have been able to do with the all LG setup. It all depends on how you had it set up. There is a control channel on HDMI that in theory allows various devices to talk to each other and control each other to some extent.
Trouble is every manufacturer seems to have invented their own dialect and sometimes devices from different manufacturers have trouble understanding each other.
But in terms of making a noise there is no reason at all why it shouldn't work.
Mind you I would not personally give house room to an all in one system. Far too many compromises for me. As you have discovered if a single element of the system goes faulty you lose the whole lot and have to replace the entire system even the bits that work perfectly. With a separates system you just replace the bit that has died which can work out much cheaper in the long run. Also you can upgrade a bit at a time rather than have to throw away the entire system just to move from, say, DVD to Blu-Ray.
