Starter woes AGAIN

[SuffolkD at aol.com]

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Subject 200 20V avant during the last cold snap:
Start in 39 degree garage, drive 130 miles.
Park for 4 hours.
Come out to start car for return trip Click.
Get weird faint sound from dash? area like some electrical gremlin.
Call AAA for jump.  Battery checks out okay.
Tow out of up hill driveway $60.  Roll down hill and let clutch out, drive
home.

Do following test:  During drive home on downhill interstate, push in clutch,
coast ~70MPH, turn off car with key, turn key to access so dash lights and
power come on, check gauges, tach at 0, turn to engage starter by key, dash
goes dim. Let clutch out -in first - just kidding.......drive home.  This
confirms binding starter to me.
Park on hills for a week.
Replace starter with used at shop $70.
Drive around feeling problem solved for six starts and a few days.
Drive 130 miles.  Park on downhill. (lesson learned or driveway was full?)
Two days later go to start. 20 degrees - Click.
WTF Roll down hill, let clutch out, etc., except I have to tighten PS belt so
I stop on downhill slolpe under street light to work on PS.  Turn off car.
But this time it starts by the key (idled) warm for 25 minutes.

3 ideas:
1. Ignition/Starter Key switch
2. Some relay gone bad -
QUESTION:  IS there some relay or other area to inspect?
3. New (used) starter has flat/dead spot on contacts.
Any help would be greatly appreciated.
-Scott in BOSTON