So, you have done everything you know to do, and everything anyone has suggested.

But you also admit the car has the original battery - and you are experiencing what could be described as an odd electrical problem and you STILL won't change the battery?
An old battery can cause all SORTS of troubles with these (and many other) cars.

I'd run to AutoZone and replace that battery now - if it does not cure the problem, you are out nothing, since it is at end of life anyway. Of course, if it DOES cure it - your permagrin is back right away.