Intermittent starting - '85 740 GLE

Hello everybody –

I'm having a problem with intermittent starting on my '85 740 GLE. The
day before yesterday, when I left my house to go to work in the AM,
the car wouldn't start. The lights on the dash came on nice & bright,
but the motor didn't turn over – I got nothing. I took mass transit to
work, and tried the car again upon returning home late that night...it
started up immediately. It started again the next day before work,
started fine again that day after work, but was dead again this
morning. Same thing – dash lights on, no motor turnover. Only a slight
click. Weather has been dry; temps have ranged between the high 50s
and mid 80s.

The battery is relatively new (replaced last Feb.), so I'm not sure
that has anything to do with it. It doesn't stall or anything after
it's started (although I haven't driven it much since the problem
started occurring, only to and from the local transit stop); it did
stall unexpectedly while driving once last winter, but hasn't done it
since.

One thing to note: Recently, the driver's side power window stopped
working. Last weekend (2 days before this latest misbehavior started),
I took the panel off of the door, tightened the screws for the window
glide, disconnected the driver's side window connector and tried
connecting it to the passenger side window switch (on the 4-switch
unit). It worked, so I left it that way until I can get a replacement
switch unit. I can't imagine that something I did when fooling with
the door would have affected the car's ability to start, but it's an
interesting conicidence that this starting problem began right after I
did this. Also - the car's previous owner installed a kill switch
which operates from the foglight switch on the dash. I'm wondering if
my fooling with the window switch could have affected the kill
switch's wiring in any way?

Any ideas? I'm obviously extremely non-mechanical and have no
intention of trying to fix this myself (unless it sounds like
something extraordinarily simple, like replacing a fuse), but I'd like
to be somewhat informed when talking to the mechanic.

Thanks much in advance - Alison