coincidence maybe lightining would'nt affect hdmi connections unless the tv was connected to an aerial/satellite dish and received a shock or partial shock and damaged the tv i'm guessing that the scart connection was not  used during the storm and the vga is from your pc/laptop

if the other devices are ok i would'nt have thought that the ac spiked as they would be damaged as well everything being on a ring main if the tv works with no connections other than aerial or dish then it possibly isn't the tv is this a new setup or an existing one are the hdmi cables ok

I would suspect the spike was from the TV cable, but I am surprised that your cable TV box survived (or do you know if HDMI out on that one is OK).

Since it's only possible to use one HDMI at a time on the TV, I guess all 3 ports are probably just connected by a switch to one common port, which maybe damaged.

Whether it's a small or a big repair you need a service technician to evaluate I think.

For Sony designers however I suggest better spike protection on HDMI should be evaluated, since your involuntary field test clearly shows a weak spot.

if the pcb has received a spike there could be burn marks on it if the ic is on a socket it could be replace if not the whole unit needs changing