Do you get sound when playing the am/fm tuner?
You say the HDMI board heats up. Have you tried using other inputs?
Have you tried a factory reset?
Onkyo | Factory Reset Of An TX-NR609 (and other)
I do see a lot of broken Onkyo receivers donated at my local Goodwill. Rarely do I see Yamaha or Pioneer. If those brands are donated, they're older models but they usually work fine.