Much sage advice from readers — many, many thanks to all.
Bottom lines:
(a) My monitor is dying. When it starts to smoke, I should definitely
switch it off. (It was manufactured in Oct. 2000 so I guess I can’t
complain.)
(b) In the meantime — an anti-glare screen is called for. Or a cheapo
replacement from Salvation Army or other discard stores to fill the gap.
(c) ON NO ACCOUNT SHOULD I, OR YOU, OR ANYONE, OPEN UP A MONITOR. There are
capacitors in there carrying 000s of volts. I could, actually and
literally, get killed. Bad, bad, bad idea.