THANKS, everyone, for the very thoughtful and thorough responses!
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John KD5YI wrote:

Check for a slide switch on the back that switches from internal to external antenna.

Would that be the ATT 0dB - 20dB switch? They show it in a figure,
but don't say what it's for. I'll try it.

Sal wrote:

Feedback to me would be nice. A Nobel Prize would be a bonus.

Your detailed suggestions of the antenna connections and
troubleshooting are quite helpful. I will return to them if the new
configuration doesn't work.

Jim Higgins wrote:

Why aren't you connecting the antenna to the Lo-Z SO-239 connector
instead of the Hi-Z Motorola type connector? (Other than the manual
telling you to use the Hi-Z.)

Right. Apparently, Radio Shack improved the DX-394, but kept the
crappy manual. Getting the antenna higher would help, I'm sure, but
for now I'm stuck with what I've got.

Richard Clark KB7QHC wrote:

If you read this last paragraph closely, it gives a clue to a project
you and your son could engage in: constructing a tuner from parts.

I appreciate the suggestions. But I'm going to take the easy way for
now.
_________________________________

These have led me to try another configuration; what I'm imagining is
at http://i258.photobucket.com/albums/h...antenna2-1.jpg

The lightning arrestor I'm considering is at http://ba-electronics.com/a28.htm.

I'm wondering:

1) if this new configuration makes sense.

2) if I should use coaxial cable at A (between the tuner and the
lightning arrestor) since the connectors are SO-239 and PL-259? Or
should I just run more of the insulated wire?

3) about coaxial cable at B (from the arrestor to the antenna wire)?

4) if this antenna tuner would be adequate? MFJ-16010 at
http://www.universal-radio.com/catal...amps/1329.html. If not, any
other recommendations?

Thanks again!

Rees