>Naturally, unplugging the wall adapter (or using a "cheater",
>which only has the hot and neutral but no ground pin)
>eliminates the hum.

When I first read this I thought you were using only a 2 pin mains cable,
but then on re-reading it I realised that is what you were doing with the
"cheater" which I know as a "earth breaker".

>This worries me.  I fear that it represents shoddy isolation
>between the laptop and the wall, i.e., that one of the 3
>connectors (inner sleeve, outer sleeve, and center pin) is a
>direct line to my house's ground.

I have an 8600c and managed to blow up the power supply sufficiently that it
would no longer charge the battery. I ended up with a replacement supply,
and Dell did not take the old one away, as they are unrepairable - well only
in that you cannot reassemble the case without it being obvious that it has
been opened. The negative side of the supply is attached to the mains ground
pin through the supply.

The centre pin goes to a Dallas 1-wire chip, mine has the part number DS2500
on it, which I think is a ROM version of the 2400. DO NOT connect the centre
pin to the inside of the barrel of the connector (which is what I managed to
do) as it connects the 19V supply directly to the Dallas chip and blows it
up. If this happens the notebook can no longer identify the power supply,
and then will not charge the battery, as it can no longer identify the
current capacity of the power supply.

My replacement power supply is a PA-12 (the original is a PA-10), so I have
not gone attempting to find the ID of the new PS, but I would like to find
out the ident of the PA-10 to get this other one back up and running, as it
then saves me carrying a PS between work and home. It should be easily done
without turning the PS on with something that can deal with 1-wire comms.

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