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Removing all the cables / power leads & unplugging it all from the mains for a while fixed an issue with my old Sky setup years ago too I recall - was in a rage on the phone to tech support as I was in the middle of watching some vitally important Finnish 3rd division women's football match or suchlike, after frantically shouting at the guy that I had turned it off & on 10 times already he told me very calmly & politely that I had to take all the cables out and unplug from the mains for a few minutes to let all the electrical components properly discharge or something to that effect - then he stayed on the line making sympathetic noises until I was done faffing around down the back of the tv & sure enough it worked a charm, I was tempted to to lie & tell him it didn't work then hang up, but by this time he was probably marching round the tech support office in his pants giving out high 5's so I couldn't take that away from him.
A totally different setup but I had problems connecting my Cambridge Yoyo to my tv via the HDMI ARC when I first got it - was just as flaky as you're describing, could not get it to play through certain inputs & even then the volume sync was fucked - eventually solved it by disconnecting every single possible connector & power lead and leaving it for a while, then connected everything back up before switching it all back on again, started working perfectly - no lag, nothing, switches perfectly every time I change source now & volume sync is back - dunno what was up but that seemed to work.