I would try to follow cables from system to system to see what is sending data to what location.
As an example, Sometimes you can as listed above bring audio + video to the TV with an HDMI cable from the TV you can feed line level or digital audio back into the receiver.
By the same right, Some receivers will take the HDMI and pass the video out on another HDMI cable. The receiver becomes your HDMI switch allowing many devices to connect to it while only needing one hdmi cable to the tv.
If you are going the analog route(line level), some TV's have an option to make the line out always on at full volume so it is not linked to the TV volume(a power out may have changed this setting). This would be in the TV menu.
Is the DVD player a...