Static damage is a possibility but I've never managed to damage a Laser from a Player of this vintage.
Modern electronic equipment seems to be much more susceptible to Static jolts. I'm led to believe it is a cost saving exercise by the manufacturers of 'chips' etc, not putting as much protection in modern devices placing the onus on the technicians fitting/replacing them to be fully 'Anti-Static'd up'.
It is odd that both now display the same symptoms.
I am going to guess you have checked and double-checked all the ribbon cables and connectors you must have had to un-plug and plug back in. Were there and Flexible PCB Ribbons? I would assume the Laser ribbon was. It may be worth checking this with a magnifier. I have had some of the connectors become detached from the stiff end piece and cause all sorts of problems.
If you get really stuck I am in Oxford too (well, just outside, Wheatley) and used to work for a Panasonic ASC repairing these things for a living. Perhaps one Sunday you could bring them over and I'll take a look. Maybe not while you wait, it depends how untidy my workshop (shed !!) is
Send me a PM. I am away this next weekend (I work Saturdays, my weekends are Sundays and Mondays) but I think free after that for a bit.
Jim.