My name is ***** ***** I will assist with your query today.
Auto tune will only discover terrestrial channels, so anything connected by HDMI or SCART would be unaffected by auto tune.
It sounds to me the HDMI \ SCART sockets may be lose, I wouldnt worry about the flickering of the TV when it turns on, its most likely scanning through the different sources (terrestrial, HDMI, SCART etc to find a signal).
You may find the manual useful which can be found at the bottom of the page here.
With regard to troubleshooting to get this working again, have you tried using both SCART and all 4 HDMI ports (including the one of the side of the TV) to connect the playstation?
Its unlikely the factory reset caused the fault, I am wondering if when you moved it to plug in the virgin HDMI if something shorted out, and the fault wasnt realised until the TV was switched off and back on as part of the factory reset.
I take it when you press the volume up or source button on the side of the TV, you dont get any response (see anything shown on the display)
This doesnt sound like a software fault but a hardware one, if you provide me with your postcode i can recommend a suitable service centre in your area.
If there is a short on the AV side of the board, it would give a fault, as the main board will turn the TV on but the faulty input would then cause a problem for the signal processor.
If the factory reset has corrupted the ROM chip (which is the other possibility) this too would require a replacement control board, as you cant re-flash the ROM chips with the software once they become corrupt.
The advise is to take the unit into a service centre as your TV has a hardware fault, this is not something you can repair yourself. If you do not wish to provide your postcode for me to recommend a service centre there is very little I can offer you over and above this.
I would suggest you use Armstrong Video Services on*********** who are within 5 miles of your postcode.
They charge a £30 fee to inspect the TV, find the exact fault (but they think it requires a new main board). If you drop it off today, they should get back to you by tomorrow afternoon.
To have the TV repaired they estimate it would cost in total £100 including the inspection fee.