My 1994 Pathfinder SEV6 has three absolutely bizarre electrical
problems that have me baffled.Before I ring up a fortune by
bringing it to the shop, I'd appreciate any advice you might have
on what the cause(s) of these strange symptoms could be:

1. "DOOR OPEN" LIGHT. When the engine is on, the Door Open
warning light always stays lit on the dashboard. When the
engine is off, the Door Open warning light goes off, but the
lights in the driver and passenger footwells remain on (as well
as the dome light, I believe) as if the door were open. This
recently caused my battery to drain.

2. INTERMITTENT STARTING PROBLEM. On occasion when
I turn the key to start the engine, nothing happens--no click,
no dash warning lights lighting up. After another try (sometimes
several), the engine will start. Here's something odd--on two
occasions when the Pathfinder wouldn't start, I turned the
headlights on, then off, and after that the engine started. Is
this a coincidence?

3. DOOR-LOCK MALFUNCTION IN COLD WEATHER. Once
we get cold weather, I can count on our electronic door locks
to malfunction. Two things typically happen: when you close
a door, it may cause all four door-lock buttons to snap down,
locking you out of the vehicle. If the vehicle is already locked
and you use your key to open the driver's door, the door-lock
button will pop up, then snap back down. I've learned to get in
by turning the key to the right and holding it as the door-lock
button clicks a few times and tries to move into the "locked"
position. After 4-5 tries the button gives up and remains open.
(Someone suggested this might be a bad latch assembly--
does that sound right? Is it easy to test for this, and is it
not extremely difficult to replace?)

Help!